Question 4. Score: 1/1 x² - 32x² Let f(x) = = 5 (a) Use the definition of a derivative or the derivative rules to find 3 f'(x) = 4x 5 64x 5 (b) Use the definition of a derivative or the derivative rules to find f" (x) = = 12x 5 64 5 (c) On what interval is f increasing (include the endpoints in the interval)? interval of increasing = [-4,0] U [4,∞) (d) On what interval is f decreasing (include the endpoints in the interval)? interval of decreasing = (-00,-4] U [0,4] (e) On what interval is f concave downward (include the endpoints in the interval)? interval of concave downward = -4√3 4√3 3 3 (f) On what interval is f concave upward (include the endpoints in the interval)? interval of concave upward = -00, -4√3 3 4√3 ,00 3

Graph of f" +x 8. The graph of f", the second derivative of the function f, is shown above. Which of the following could be the graph of f?

How do you find the derivative of f(x) = 5 - |x-5| ?

How can you sometimes identify a function ƒ(x) by knowing ƒ'and knowing the value of ƒ at a point x = x0? Give an example.

10-Please circle the answer

If the handwriting font, please write the font clearly, otherwise I can't understand it, please

A company's annual revenue after x years is f(x)=x²-9x² +15x +29 thousand dollars (for x 20). (a) Make a sign diagram for the first derivative Select Make a sign diagram for the second derivative. Soled Select (b) Sketch the graph of the revenue function, showing all relative extreme points and inflection points. 30 35 30 25 20 NANA 15 10 6 35 25 20 15) 10 (c) Give an interpretation of the infection point. 6 35 20 15 10 The decline in revenue first begins to slow at the inflection point. O The company reaches minimum revenue at the inflection point. O The increase in revenue first begins to slow at the inflection point. O The company reaches maximum revenue at the inflection point. Onone of these 4 2 35 25 20 15) 10 4

Find the derivatives

Consider the function f and its derivatives below. f'(x) = -2(2³-32) (³+64)² 6x²(³-128) (3+64)3 f"(x) = f(x) = 3 +64 Fill in the table below. For answers that require intervals, use interval notation and write your answer as a comma-separated list of intervals that are as inclusive as possible. Write "NONE" as your answer, if appropriate. Your answers must be exact or accurate to two decimal places. 2 1.26 38=2 4 1.59 16 2.51 √32 3.17 equations of vertical asymptote(s) of f: equations of horizontal asymptote(s) of f: f is decreasing on: f is increasing on: z-coordinate(s) of each local minimum of f: z-coordinate(s) of each local maximum of f: f is concave down on: f is concave up on: 01 x-coordinate(s) of each inflection point of f: √64=4 128 5.04 Sin den Ja

Make a sign diagram for the derivative of the function. f(x) = x +4x³8x² +62 f'(x) increase decrease x = Sketch the graph of the function. y O -4 f'(x) Find all open intervals of increase and decrease. (Enter your answers using interval notation.) -2 -2 50 -50 y 0 50 f'(x) AN 4 -4 -2 -50 x = 2 f'(x) 0 f'(x) y 50 -50 y JAAL X 4 -4 50 2 -50 x = 2 f'(x) 4 0 X