Question

help with calculus please!

Answer 1

From the chain rule... h'(x) = f'(g(x))*g'(x). Since f and g have linear slopes at the points they're asking for, you can just do some basic algebra--just eyeballing it g'(x) = -1 and f'(x) = 2 for [0, 4) and -2 for (4, 8]

So, plugging everything in, h'(2) = f'(g(2))g'(2) = f'(6)*g'(2) = -2*-1= 2

Same logic works for h'(6), just try to keep it straight in your head:

g(6) = ?
f'(g(6)) = ?
f'(6) = ?

Answer 2

so would a = 2 and c = -6?

Answer 3

a = 2, as I showed above

For c you have g(6) = 2 (just eyeballing), f'(2) = 2 ("the slope of f at x = 2") so f'(g(6)) ("the slope of f at g of 6")= 2, then multiply by g'(6) = -2 (the slope of g at x = 6) so your answer is f'(g(6))g'(6) = 2 * -2 = -4.

Answer 4

oh i was confused on the eyeballing parts; i thought it was plugged in because of the first h'(2) = ... thank you !

Answer 5

oh wait i got -4 for c before and it said it was wrong?

Answer 6

It's a really confusing problem. h'(6) = f'(g(6))g'(6) = f'(2)g'(6) =2*-1 = -2, that was my fault whoops

Answer 7

ok ty!