Show that the function is increasing and decreasing on the given open intervals. (Enter your answers as a comma-separated list if necessary.) y = x + 2; decreasing on (-*, 0); increasing on (0, ∞) We have y'(x) = x = . Therefore, the critical numbers are = y'(x) 0 when x = and y'(1) = . Finally, since y'(-1) = on (x, 0) and increasing on (0, ∞). ' we have that y is decreasing

Find f. f"(x)  =x6 - 4x4 +x +1

A graphing calculator or computer algebra system is recommended. f'(x) and its graph are given. Use the graph of f'(x) to determine the following. f(x)=x²-x - 6 -6 concave up -4 concave down X = y 10 Ⓡ (a) Where is the graph of f(x) concave up and where is it concave down? (Enter your answers using interval notation.) 2 (c) Find F"(x). f"(x) = 4 X (b) Where does f(x) have any points of inflection? (Enter your answers as a comma-separated list.)

If f(x) = 5 + 5T. Find f-'(- 5) =

Let f(x) = f(-1) = = f(-5) = f(-6) = 8x - 2, -x², X ≤ -5 X > -5' Find f(-1), f(-5), and f(-6).

Suppose that f(x) and g(x) are two functions and we know that: f(-3) = 2 g(-3) = 5 f'(-3) g'(-3) Find the following: (ƒ − g)'(−3) = (g - f)'(-3) = -1 -2 == (fg)'(-3) = (4) - '(-3) = f(x) x² If k(x) = = = then k'(-3)

Suppose f(x)=x^4+3x+1 on the interval [−4,−1]. Find x when f′(x)=0.

If f*(x) = ²x² + x² 2 Ox= -3 Ox= -1 Ox=0 Ox=1 N/W -3, determine the x-value(s) where f(x) changes from concave up to concave down.

(2x + 1)3 (1 – 4x)2' find f'(x) and fully simplify. 2. If f(x)

Differentiate.