Question

Here is the graph of a certain function f.
Sketch the graph of its derivative f'.
refer to the attachment.

Answer 1

I just redrew the graph of f again.

Note: for x<0 , the graph flattens out

Also for x>5, the graph flattens out.

Answer 2

Go along the graph and mark in the sign of the derivative (slope) at every point, Note: at x=3 there is a cusp , the derivative does not exist there (which means we will have a vertical asymtote at x=3 on our graph of the derivative.

Answer 3

Note: for x<0 , the derivative will be zero (as the graph of the function is flat).

Answer 4

for 0<x<3 , the derivative will be negative (and will be getting increasingly negative as you get to x=3)

Answer 5

at x=3 there is a vertical asymtote.

Answer 6

for x>5, the derivative is zero.

Answer 7

for 3<x<5, the derivative is positive but gets smaller and smaller. .

Answer 8

It looks a bit like a shifted hyperbola but not quite.

it is zero for x<0 and x>5 , and then it looks like a hyperbola in 0<x<5.