Question

Assume the function f(x) shown is the derivative of some function g(x).
a) Tell where g(x) is increasing.
b) For what value of x does g(x) have a relative minimum?
c) Describe the behavior of g at x = 4. Explain how you know this would be true.

See attached.

Answer 1

\(g\) is increasing on the intervals where \(f>0\) i.e . where \(f\) is above the \(x\) axis

Answer 2

Can someone explain both b and c, please

Answer 3

relative min means the function goes from decreasing to increasing

Answer 4

that means the derivative goes from being negative to positive
look to see where the derivative crosses the \(x\) axis going from below it to above it

Answer 5

looks like it does that at \(x=2\)

Answer 6

so at f(2) g(x) has a relative minimum?

Answer 7

right... so then

Answer 8

yes, function goes from decreasing to increasing

Answer 9

btw it is not at \(f(2)\) it is at \(x=2\)

Answer 10

at x = 4 g(x) switches from increasing to decreasing, does that mean g(x) is concave down

Answer 11

I mean f(x)*

Answer 12

at \(x=4\) the function is still increasing (because the derivative is positive there)

Answer 13

yes, \(f\) goes from increasing to decreasing, so you are right, the function goes from being concave up to concave down

Answer 14

Okay, cool. Thanks again

Answer 15

it doesn't mean the function is concave down, it means it changes concavity there
yw

Answer 16

Yeah, I know, should have clarified