Question

Composite function help?

Answer 1

I don't understand the question

Answer 2

There's quite a bit of information you must extract

But let's break it down

(i) y = g(x) has a tangent of y = 2x - 2 when x = -5
So what is g'(x) when x = -5 based off the tangent? i.e. find g'(-5)

(ii) f(x) = -3g(x) + 5x + 5
Now f'(-5) means you differentiate f with respect to x and then evaluate this derivative f' at x = -5. N.B. A common mistake people make is to sub in x = - 5 before differentiating.
Always differentiate first!

So f'(x) = -3 g'(x) + 5
Sub in x = -5 and you'll work it out from your result of (i)

Answer 3

g'(-5) = -12 right?
Im a little lost.
Wouldnt it be:
-3(-12)+5

Answer 4

Would B be the correct answer to this? @agent0smith

Answer 5

Your work above looks right

Answer 6

@legomyego180 no, g'(-5) is actually 2 (the gradient of the tangent at that pt). Recall the gradient of the tangent the curve f at the point x= a is f'(a).

Then you sub in this g'(-5) into the second expression

Answer 7

ah I see how you got your g'(-5)= -12 from. you subbed in x = -5 into the tangent equation.

Wrong. What this does is find the y coordinate of the function. This would be useful if they asked, at what point does the tangent meet the function?
However, it does not describe the derivative, or gradient of the tangent at that pt. Be sure to make clear distinction between these! Tangent line eqn not the same as derivative!

Answer 8

Oh yeah you want the slope, which is the slope of the tangent line, which is 2.