# Application of derivatives Questions and Answers

Calculus
Application of derivatives
Find the critical points and classify them as local maxima, local minima, saddle points, or none of these. f(x, y) = (x+y)(xy + 9) (x, y)=________ (smaller x-value) (x, y) =_______ (larger x-value)
Calculus
Application of derivatives
The revenue from sales of x units of a product is given by R(x) = 200x-0.01x², and the cost of producing and selling the product is C(x) = 38x+0.01x² + 16,000. Producing and selling how many units will result in a profit? Producing and selling between________ and______-units of the products will result in a profit.
Calculus
Application of derivatives
(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius is 38 m?
Calculus
Application of derivatives
A model used for the yield Y of an agricultural crop as a function of the nitrogen level W in the soil (measured in appropriate units) is Y=KN /25 + N² where k is a positive constant. What nitrogen level gives the best yield?
Calculus
Application of derivatives
Divide. (-10x³+7x-5)÷(2x²-3) Write your answer in the following form: Quotient +
Calculus
Application of derivatives
(-7x4+5x³+20x²+10)÷(-x²+x+3) Write your answer in the following form: Quotient + -7x4+5x³+20x² +10 -x²+x+3 = + 2 -x + x + 3 Remainder 2 -x+x+3 X S ?
Calculus
Application of derivatives
Determine if the following function is concave up or concave down in the first quadrant. y=5x^2/3 Is the function y=5x^2/3 concave up or concave down in the first quadrant? Concave up Concave down
Calculus
Application of derivatives
Determine whether the function y = -2x³ is increasing or decreasing for the following conditions. (a) x < 0 (b) x > 0 (a) Is the function increasing or decreasing for x < 0? decreasing increasing
Calculus
Application of derivatives
The annual total revenue for a product is given by R(x) = 30,000x – 5x² dollars, where x is the number of units sold. To maximize revenue, how many units must be sold? What is the maximum possible annual revenue? To maximize revenue,_________units must be sold. (Simplify your answer.
Calculus
Application of derivatives
Let h(x) = -9x - 13 - 6x²- x³ Determine the absolute extrema of h on [-4, 0]. If multiple such values exist, enter the solutions using a comma-separated list. The absolute minimum of h is_______and it occurs at x =_____ The absolute maximum of h is_______and it occurs at x =_____
Calculus
Application of derivatives
Consider h(v) = 7v log5( – 6v) on [ – 125/6 ,-1/6] Determine the interval over which h is continuous and the interval over which h is differentiable. h is continuous on _______ h is differentiable on _______ - Use the above information to determine if the Mean Value Theorem may be applied to h over [ – 125/6 ,-1/6]
Calculus
Application of derivatives
Find the points on the curve y = x³ + 3x^2 - 9x + 8 where the tangent is horizontal. smaller x-value (x, y) = larger x-value (x, y) =
Calculus
Application of derivatives
4 ln(x + 6) x + 6 Let f(x) Determine the absolute extrema of f on [-5, -1]. If multiple such values exist, enter the solutions using a comma-separated list. The absolute minimum of fis +2 The absolute maximum of f is and it occurs at x = and it occurs at x =
Calculus
Application of derivatives
Let h(x) - 52 +9 Determine the absolute extrema of h on [-3, 3].
Calculus
Application of derivatives
Let g(x) = 17 + 24x + x³ + 9x² Determine the absolute extrema of g on [-5, -1]. If multiple such values exist, enter the solutions using a comma-separated list.
Calculus
Application of derivatives
Let h(x) = x² + 21 + 10x Determine the absolute extrema of h on [- 7,2].
Calculus
Application of derivatives
For the polynomial below, -3 is a zero. g(x)=x²³ - 2x² - 9x + 18 Express g (x) as a product of linear factors.
Calculus
Application of derivatives
7. (Factoring) Factor the difference of squares. a) x² - 121 b) 9m² - 4n²
Calculus
Application of derivatives
(1 point) 3sin(x)tan(x)+3¯¯√sin(x)=0 Find all angles in radians that satisfy the equation. For each solution enter first the angle solution in [0,π) оr [0,2π) (depending on the trigonometric function) then the period. When 2 or more solutions are available enter them in increasing order of the angles. (e.g. x=π/2+2kt or x=3π/2+kπ etc.) Note: You are not allowed to use decimals in your answer. Use pi for π.
Calculus
Application of derivatives
For the polynomial below, 3 is a zero. g(x)=x²- 4x² + x + 6 Express g (x) as a product of linear factors.
Calculus
Application of derivatives
For the polynomial below, -3 is a zero. f(x)=x³ - 3x² Express f(x) as a product of linear factors.
Calculus
Application of derivatives
A spherical balloon is inflated at the rate of 67 cm³/sec. At what rate is the radius increasing when r = 4 cm?
Calculus
Application of derivatives
Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always two times its height. Suppose the height of the pile increases at a rate of 3 cm/s when the pile is 17 cm high. At what rate is the sand leaving the bin at that instant?
Calculus
Application of derivatives
Find the extrema of y = x³-6x² +9x+2 on [0,2]. (Notice this is the same equation as #4a.) Label max/min.
Calculus
Application of derivatives
Find the unit tangent vector T(t) at the point with the given value of the parameter t. r(t) =(t²- 3t, 1 + 4t,1/3 t^3+1/2 t^2) ,t = 3 T(3)=
Calculus
Application of derivatives
Find the profit function if cost and revenue are given by C(x) = 178 +4.9x and R(x) = 7x -0.05x². The profit function is P(x) =
Calculus
Application of derivatives
Find an equation for the surface consisting of all points that are equidistant from the point (-3, 0, 0) and the plane x = 3. Identify the surface. O parabolic cylinder O hyperbolic paraboloid O hyperboloid of one sheet O circular paraboloid O hyperboloid of two sheets O ellipsoid O elliptic cylinder O cone
Calculus
Application of derivatives
Find all local extremes of the function f(x, y) = (x² + y²) e^x²-y²
Calculus
Application of derivatives
Find the marginal cost function. C(x) = 190 +3.9x -0.03x²
Calculus
Application of derivatives
The total cost (in dollars) of producing x food processors is C(x) = 1900 + 30x -0.1x². (A) Find the exact cost of producing the 91st food processor. (B) Use the marginal cost to approximate the cost of producing the 91st food processor. (A) The exact cost of producing the 91st food processor is \$_______ (B) Using the marginal cost, the approximate cost of producing the 91st food processor is \$______ *
Calculus
Application of derivatives
For f(x)=1/5+x²4the slope of the graph of y = f(x) is known to be -4/81 at the point with x-coordinate 2. Find the equation of the tangent line at that point. _____(Type an equation. Use integers or fractions for any numbers in the equation.).