Question

correct my answer please?

Answer 1

g'(f(x))*f'(x) = g'(f(4)*f'(4)

Answer 2

f(4) = 8

Answer 3

so g'(8)*f'(8)?

Answer 4

so x = 16 and the slope is -1

Answer 5

so is u'(4) = -1?

Answer 6

to do this problem you need g(x) and f(x)
g(x)= -x + 16
f(x) = 2x for 0≤x<8

g'(x) = -1
f'(x) = 2
g'(8)*f'(4) = -1*2 = -2
notice that because g' and f' are constant, the x values are irrelevant for this problem.

for u(12) we must use a different function for f(x)

Answer 7

okay so then u'(12) = 1 correct?

Answer 8

i mean -1 , sorry

Answer 9

wait no it must be 2 !!

Answer 10

i get it now :) ty guys!!!

Answer 11

what are you using for f(x) when x>8 ?
it should be
f(x)= -2x + 32

notice f(8)= 16, and f(16) =0, as it should

g(x) =-x + 16

as a check, we can form
u(x)= g(f(x)) = -( -2x + 32)+16 = 2x -16
and u' = 2
(independent of x)

using the chain rule, you should get the same answer.