a) ƒ' (x) = = 1 for all 0 ≤ x ≤ 4. b) f'(x) > 0 for all 0 ≤ x ≤ 4. c) f' (3) = 0 d) f' (3) = 1 > > >

Sketch a graph with the following characteristics: f'(x)>0,  -inf<x<-1,  1<x<3 f'(x)<0,  -1<x<0,  0<x<1,  x>3 f"(x)>0,  0<x<2,  4<x<inf f"(x)<0,  -inf<x<0,  2<x<4 f'(-1)=f'(-1)=f'(3)=0 f"(2)=f"(4)=0 lim x approaches inf  f(x)=0 lim x approaches 0^- f(x)=-inf

Solve only D)

Let f(x) ƒ'(x) = ƒ'(1) = = = 3x² + 3x + 2 OF

Sketch the graph of a function that satisfies all of the given conditions. f'(0) = f'(2) = f'(4) = 0, f'(x) > 0 if x 4, f"(x) > 0 if 1 3

Pls help ASAP

The graph of the first derivative f' of a function f is shown. (Assume the function is defined only for 0 ≤ x ≤ 9.) y = f'(x) निकित 2 6 8 y X = (a) On what interval(s) is f increasing? (Enter your answer using interval notation.) [0,1) U (2,3) U (5,7) X X (b) At what value(s) of x does f have a local maximum? (Enter your answers as a comma-separated list.) 1,3,7 At what value(s) of x does f have a local minimum? (Enter your answers as a comma-separated list.) x = 0,2,5,9 X (c) On what interval(s) is f concave upward? (Enter your answer using interval notation.) On what interval(s) is f concave downward? (Enter your answer using interval notation.)

if f' is continuous, f(3)=0, and f'(3)=7, evaluate lim x to 0  f(3+5x) + f(3+6x)/x

How would I calculate this not on a closed interval? (Using Mean Value Theorem)

' Find f -() for f(x) =,* < 0. 5 ,X < 0. %3D f -'x) =