Let f(z) = x² - 128x² 5 (a) Use the definition of a derivative or the derivative rules to find f'(x)= 4x³ 256x 5 5 (b) Use the definition of a derivative or the derivative rules to find f"(x) = 12x 5 256 5° below (c) On what interval is f increasing (include the endpoints in the interval)? interval of increasing = (-0,-8) u (0,8) (d) On what interval is f decreasing (include the endpoints in the interval)? interval of decreasing= (e) On what interval is f concave downward (include the endpoints in the interval)? interval of concave downward = (f) On what interval is f concave upward (include the endpoints in the interval)? interval of concave upward Submit Question esc @ $ % 1 2 3 M

Explain the relationship between the slope and the derivative of fx at x=a.

Find the derivative of the function. f(x) - (2x³ - 8x?+7)" 8x² + 7)*

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