Given f(x)= x³-12x+5, find all local maxima and local

A constant volume of cookie dough is formed into a cylinder with a relatively small height and large radius When the cookie dough is placed into the oven the height of the doug the radius increases but it retains its cylindrical shape At time t the height of the dough is 10 mm the radius of the dough is 16 mm and the radius of the dough is increasing a per minute Part A At time t at what rate is the area of the circular surface of the cookie dough increasing with respect to time 5 points Part B At time t at what rate is the height of the dough decreasing with respect to time 5 points

Step 1 To determine the intervals on which the function is increasing or decreasing first find the critical numbers of the given function Determine g x g x x 2x 360 g x 2x 2 Step 2 To determine the critical numbers of g x set g x equal to zero and solve for x g x 0 2 x 11 2x 2 0 g 0 g 0 20 g 0 0 Step 3 Since there is no point for which g x does not exist x 1 is the only critical number Thus the number line can be divided into two intervals 1 and 1 Determine the sign of g x at one test value in each of the two intervals X First consider the interval 1 Let x 0 g x 2 x 1 1 2x2 0 1 1 1 Step 4 Since g 0 0 for which interval is the function decreasing Enter your answer using interval notation 0 1 00 1 Step 5 Now consider the interval 1 Let x 2 g x 2 x 1 g 2 2 g 2 2 1

To test an individual s use of a certain mineral a researcher injects a small amount of a radioactive form of that mineral into the person s bloodstream The mineral remaining in the bloodstream is measured each day for several days Suppose the amount of the mineral remaining in the bloodstream in milligrams per cubic centimeter t days after the initial injection is approximated by C t 2t 3 1 2 Find the rate of change of the mineral level with respect to time for 7 5 days The rate of change of the mineral level with respect to time for 7 5 days is approximately Round to two decimal places as needed milligrams per cubic centimeter per day

If the price charged for a bolt is p cents, then x thousand bolts will be sold in a certain hardware store, where p = 66- x/36. How many bolts must be sold to maximize revenue? A. 1,188 bolts B. 2,376 bolts C. 1,188 thousand bolts D. 2,376 thousand bolts

Suppose that f(4) = 3, g(4) = 4, f'(4) = -5, and g'(4) = 2. Find h'(4). (a) h(x) = 3f(x) + 2g(x) h'(4) = (b) h(x) = f(x)g(x) h'(4) = (c) h(x) =f(x)/g(x) h'(4) = (d) h(x) =(g(x))/(f(x) + g(x)) h'(4) =

A person standing close to the edge on top of a 80-foot building throws a ball vertically upward. The quadratic function h(t) 16t^,2 +64t+ 80 models the ball's height about the ground, h(t), in feet, t seconds after it was thrown. a) What is the maximum height of the ball? feet b) How many seconds does it take until the ball hits the ground? seconds

Find the derivative of the function. h(x) = log3 x√x - 7/6 h'(x)=

Let z₁ and z₂ be two complex numbers satisfying (z-w)²+(z-w²)² = 0, where w is non real cube root of unity. Also let 'a' be a variable point on the circle |z+1/2|=√3/2 and a₁, a2 are values of a such that lal is maximum and minimum respectively. On the basis of above information, answer the following questions : Number of complex numbers a such that la - a₁l +|a -a₂l= √6 is

If f(x) = 2x3/3 - 3x²/2 + 4x, what is f'(x)? f'(x) = 2x³ - 3x² + 4x f'(x) = 2x² - 3x + 4 f'(x) = -2x² + 3x - 4 f'(x) = -2x³ + 3x² - 4x

Use calculus to find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.) h(x) = ex² - 4 on [-2, 2] Absolute maximum value: at x = (Enter your answers as a comma-separated list if there are multiple x-values.) Absolute minimum value: at x = (Enter your answers as a comma-separated list if there are multiple x-values.)