Suppose we have two interesting functions f and g. We have limited knowledge of them as follows: • ƒ:R → (-); f(0) = 0; f'(x) = 12 1 1-2f (¹=²) = r) = g(x) Using this information, evaluate -2f (2-3f(4-4x)). g'(1)

Solve by using Integration by parts: Show and solve for u and dv. xe?* a) (2x+1)² da dx

Consider the following. f(x) = x3 - 6x2 + 1 = (a) Find f'(x) and f"(x). f'(x) : = f"(x) : O = (b) Graph f(x), ƒ'(x), and f'(x) with a graphing utility. -5 الا y 150 100 50 -50 - 100 - 150 5 X -5 y 150 100 50 -50 -100 - 150 X -5 y 150 100 50 -50 -100 - 150 5 X

If f (x) = (2x + 1) (4x + 1), then: a. f (-2) 21 ४ b. f'(-2) =-26 ४ c. f" (-2) 16 d. The values of x for which f(x) = 0 are e. The values of x for which f'(x) = 0 are