Question

The attachment is a graph of F'(x)

(a) Find the critical values for F(x).

(b) Give the intervals where F(x) is increasing.

(c) Give the intervals where F(x) is decreasing.

(d) Find the x-coordinates of the relative extrema for F(x).
relative max:
relative min:

Answer 1

Function has 3 critical values it appears.

Answer 2

Remember critical numbers happen when f'=0
when do you have horizontal tangents?

Answer 3

7,15

Answer 4

and 0

Answer 5

2/3

Answer 6

2/3 means you got 2 out of 3 correct

Answer 7

do you have a horizontal tangent at x=15?

Answer 8

The graph is a function of F'(x), don't derivatives pass through F(x) horizontal tangents?

Answer 9

oh the attachment is f'

Answer 10

not f

Answer 11

then you are right

Answer 12

yay!, I find it harder to answer parts b,c, and d

Answer 13

f is increasing when f'>0
f is decreasing when f'<0

Answer 14

so when is f'>0 (when is the graph above the x-axis)

Answer 15

interval (7,15)

Answer 16

right so since f'>0 on (7,15) then f is increasing on (7,15)

Answer 17

oh ok. so decreasing (- inifnity,7) U (15, inifnity)?

Answer 18

because the function is below the x-axis?

Answer 19

well i might say (-inf, 0) U (0,7) U (15,inf)

Answer 20

just because at x=0 the graph is resting

Answer 21

right! thank you.

Answer 22

so how would we be able to find the relative max/min?

Answer 23

Well now you know where the function is increasing and decreasing.

When the function switches from increasing to decreasing at x=a we have a max at x=a.
If we have the function switches from decreasing to increasing at x=a we would have a min at x=a.

Answer 24

for example