Calculus
Differentiation
Let g(x) = x² + 3x - 5. Use the limit definition of the derivative to differentiate g. g'(x) =_______ Determine the slope of g at x = - 8. g'(- 8) =_______ Submit All Parts
Calculus
Differentiation
Let f(x) = ∛2 Determine the derivative of f. f'(x) = ______ Determine the slope of f at x = 2. f'(2) = _______
Calculus
Differentiation
Let g(x)= -3x² + 5 Use the alternative limit definition of the derivative to determine the derivative (slope) of g at x = -9. g'(- 9) =_______
Calculus
Differentiation
Consider the graph of f given below. Evaluate the following limit. lim △x->0 f(1+ △x) - f(1)/△x = ________
Calculus
Differentiation
Let h(y) =- √Y Determine the value(s) of y, if any, for which h has a horizontal tangent line. ○ h has a horizontal tangent line at y = □ ○ h has no horizontal tangent lines.
Calculus
Differentiation
Let f(x)=9/x² Use the limit definition of the derivative to differentiate f. f'(x)= □ Determine the slope of f at x = 11. f'(11)= □
Calculus
Differentiation
Hannah invested \$32,000 in an account paying an interest rate of 2 ¼ % compounded quarterly. Mila invested \$32,000 in an account paying an interest rate of 1⅝% compounded continuously. After 13 years, how much more money would Hannah have in her account than Mila, to the nearest dollar?
Calculus
Differentiation
Let f(x)=9x² + 4x. Use the limit definition of the derivative to differentiate f. f'(x) = □ Determine the slope of f at x = 9. f'(9) = □
Calculus
Differentiation
Let f(x) = x² - 5 Determine the equations of two unique tangent lines of f that intersect at (-5, 19). Report solutions using slope-intercept form. y =___ y =___
Calculus
Differentiation
Let h(x)=√x. Use the limit definition of the derivative to differentiate h. h'(x) = ________ Determine the slope of h at x = 1. h' (1) = ______
Calculus
Differentiation
The limit definition of the derivative Let g(x) = - 8/x-4 Use the limit definition of the derivative to differentiate g. g'(x) = □ Determine the slope of g at x = -8. g'(- 8) = □
Calculus
Differentiation
Let f(x) = -8. Use the limit definition of the derivative to differentiate f. f'(x) = ________________________ Determine the slope of f at x = -9. f'(- 9) = ________________
Calculus
Differentiation
Fit a quadratic function of the form f(t) = c₀ + c₁ t+ c₂ t² to the data points (0,7), (1, 8), (2, –3), (3, −6), using least squares. f(t) =
Calculus
Differentiation
Part 3: Suppose the field has a length of 6,000 feet. Sally buys fencing to enclose it, but has bought 4 feet too much. Rather than throwing away the extra fencing, Sally enclose a slightly larger field by enlarging each side of the field by the same amount, so the fencing encloses the field and a border: What is the largest animal that could be at point X and be entirely within the border region, touching neither the fence nor the field? a)an ant b)a mouse c)a cat d)a cow e)an elephant Part 4: Give the average rate of change of the perimeter, if the length increases from 6,000 feet to 7,000 feet:_________
Calculus
Differentiation
42)Let f(x)=x²-5 Determine the equations of two unique tangent lines of f that intersect at (-5, 19). Report solutions using slope-intercept form. y = y =
Calculus
Differentiation
Let h(x) = 1/4 x² + 5 and f(x) = -1/4 x + d Determine the equation f such that f is perpendicular to h. Report the solution using slope-intercept form.
Calculus
Differentiation
Let g(x) = (-x⁴ + 3 - 9x³)/x² Determine the derivative of g. g'(x) = _________ Determine the interval(s) on which g is differentiable. Report the solution using interval notation. g is differentiable on __________
Calculus
Differentiation
Let f(x)=2/x^1/6 Determine the derivative of f. f'(x)= Determine the interval(s) on which f is differentiable. Report the solution using interval notation.
Calculus
Differentiation
Let h(t) 4t^5 + 5t^4 -6t+ 5t³ Determine the derivative of h. h' (t)= Determine the interval(s) on which h is differentiable. Report the solution using interval notation.
Calculus
Differentiation
Let h(v) = 2v² (v⁵ + 5) Determine the derivative of h. h'(v) = ______ Determine the slope of h at v = 0. h'(0) = _________
Calculus
Differentiation
Let h(x) =x^5 Determine the derivative of h. h'(x) = Determine the interval(s) on which h is differentiable. Report the solution using interval notation.
Calculus
Differentiation
Let h(x) =1/x^12 Determine the derivative of h. h'(x) = Determine the interval(s) on which h is differentiable. Report the solution using interval notation.
Calculus
Differentiation
maximum and minimum values using Lagrange multipliers. Of all points (x, y, z) that x + 4y + 3z=21, find the one that minimizes (x-1)² + (y-1)² + (z-1)². The given function has a minimum at (____ ____ ______ )which satisfies x + 4y + 3z = 21,
Calculus
Differentiation
Let g(x)=6/∜x. Determine the derivative of g. g'(x) =[ ].Determine the interval(s) on which g is differentiable. Report the solution using interval notation. g is differentiable on [ ]
Calculus
Differentiation
Let g(x)=-1/x^4 Determine the derivative of g. g'(x)= Determine the interval(s) on which g is differentiable. Report the solution using interval notation.
Calculus
Differentiation
Let h(x) = x^4 - 7^3 Determine the derivative of h. h'(x) = Determine the interval(s) on which h is differentiable. Report the solution using interval notation.
Calculus
Differentiation
Let f(x) = 6x² - 3x + 5 Determine the derivative of f. f'(x) = _________ Determine the interval(s) on which f is differentiable. Report the solution using interval notation. f is differentiable on _______
Calculus
Differentiation
let h(t)=9t^13 -3t^-13 Determine the derivative of h. h' (t)= Determine the interval(s) on which h is differentiable. Report the solution using interval notation.
Calculus
Differentiation
Let f(x)=- 6x^11 Determine the derivative of f.f'(x)= Determine the interval(s) on which f is differentiable. Report the solution using interval notation.
Calculus
Differentiation
Find and simplify each of the following for f(x) = 4x-3. (A) f(x + h) (B) f(x+h)-f(x) (C)(f(x+h)-f(x))/h (Do not factor.)
Calculus
Differentiation
Let g(x) = 9. Determine the derivative of g. Determine the slope of g at X = 7. g'(7)=
Calculus
Differentiation
Let h(z) = -5z(⁵/²) - 9z(³/²) + 7z(¹²/¹¹) Determine the derivative of h. h'(z) = ______ Determine the slope of h at z = 1. h' (1) = ______
Calculus
Differentiation
Let f(w)=(-5w-4w^4 +3)/w^1/3 Determine the derivative of f. f'(w)= Determine the interval(s) on which f is differentiable. Report the solution using interval notation. f is differentiable on_______
Calculus
Differentiation
Let h(x) = (5 - 2x² - 6x⁴)/x⁴ Determine the derivative of h. h'(x) = ________ Determine the interval(s) on which h is differentiable. Report the solution using interval notation. h is differentiable on ____
Calculus
Differentiation
let g(x)=1/x⁶. Determine the derivative of g. g'(x) =[? ].Determine the interval(s) on which g is differentiable. Report the solution using interval notation. g is differentiable on[ ?]
Calculus
Differentiation
Calculus
Differentiation
Let g(v)=-v^(12/5) + (2)v^(7/3)-(7)v^(9/8) Determine the derivative of g. g'(v)=[?] Determine the slope of g at v = 1. g'(1)=[?]
Calculus
Differentiation
Let f(z) = (5z + 7)(-8z +9) a)Determine the derivative of f. f'(z)= b)Determine the slope of f at z = -2. f'(-2)=
Calculus
Differentiation
find the Taylor series of each function at the indicated number. Give the interval of convergence for each series. f(x)=x² In (1 + x/2) ;x=0
Calculus
Differentiation
You are constructing a cardboard box with the dimensions 2m by 4m. You then cut equal-size squares from each corner so you may fold the edges. What are the dimensions of the box with the largest volume?
Calculus
Differentiation
You want to enclose a rectangular region with 450 feet of fencing. Express A(w), the area of the region as a function of its with. A(w)=_________
Calculus
Differentiation
Find the four second-order partial derivatives for f(x,y)=4x^(7).y^(4)+3x^(5).y^(6). fxx = ___ fyy= ___ fxy = ___ fyx = ___
Calculus
Differentiation
This problem has two parts. Part 1: In 2069, a virus begins in Boston and spreads in such that the number N of people infected grows exponentially with time t. The table below shows how many days it takes from initial outbreak to have various numbers of cases. N = # of 1 2 3 cases million million million t=# of days 108 157 186 How many days until the Boston virus infects five million people? ______ How many days until there are ten million people infected by the Boston virus?______ Part 2: Enter here (using math notation or by attaching in an image) an explanation of your answers.
Calculus
Differentiation
Consider the curve parameterized by: x =2t^3/2 - 1 and y = 5t. (a.) Find an equation for the line tangent to the curve at t = 1.
Calculus
Differentiation
Consider the function f(x) = 2x² + 3x - 4 on the closed interval [-2, 1]. Find the exact value of the slope of the secant line connecting (-2, f(-2)) and (1, f(1)). m =___________ By the Mean Value Theorem, there exists c in (-2, 1) so that m = f'(c). Find all values of such c in (-2, 1). Enter exact values. If there is more than one solution, separate them by a comma. c=___________
Calculus
Differentiation
Which of the following is not a solution to sin x-cos 2x = 0 on the interval [0, 2π)? (a)π/6 (b)π/2 (c)5π/6 (d)3π/2
Calculus
Differentiation
Let g(y) = (y-6) (y + 8)/(y-7)(y-4) Determine g'(y) g'(y) =
Calculus
Differentiation
Let h(x) = f(x) · g(x) and j(x) = f(x)/g(x) x 1 2 3 4 f(x) -5 -3 5 2 f'(x) 4 3 -4 1 g(x) -3 2 1 -4 g'(x) -3 0 -4 1 Use the table above to determine the following derivatives. h' (4) = j'(4) =
Calculus
Differentiation
Let g(t) = 1/t⁸ Determine the derivative of g. g' (t) = Determine the interval(s) on which g is differentiable. Report the solution using interval notation. g is differentiable on
Calculus
Differentiation
Let f(x) = (3x + 3)/(-3-7x) Determine the derivative of f. f'(x) = Determine the slope of f at x = - 4. f'(-4)=