Differentiable Function. If a differentiable function f(x) satisfies f(-4) = f(4) then there exists a c in (-4,4) with O f'(c) > 0 O f'(c) < 0 O f"(c) = 0 O f"(c) > 0 O f"(c) < 0 O f'(c) = 0 O f(c) > 0 O f(c) = 0

Sketch the slope graph of a function f with input t that meets these criteria f(-1) 5 the slope is positive for t < 1, the slope is negative for t 1, and f'(1) does not exist |f'(t) f'(t) -1 -5 If'(t) |f'(t) 5+ 5

3x Use the Quotient Rule to differentiate the function f(x)= x' +5 3(-5+4x°) a. f'(x)= – 3(-5-4x*) (1$ + s)° b. f'(x)= 3(5+ 5x) c. f'(x)= (15 + 5)² 3(5 + 4x°) (r$ + 5)? d. f'(x) = %3D 3(5+ 6x°) (r° + s)² e. f'(x) = -

Let f be a differentiable function. We are given the following values of f and f': x|ƒ(x) | ƒ'(x) 7 Consider the functions g, h, k defined by Find the following values: a) g' (4) = b) h' (4) = c) k'(4) = g(x) h(x) k(x) 4 16 36 = = = 36 2 3 -3 4 f(x²) fof(x) 3(f(x))³ — 1(ƒ(x))²