Question

i know how to do differentiation.... but i never learned how to do it on a graph..........

Answer 1

OK, so \(h(6) = f(g(6))\). Can you see what \(g(6)\) is?

Answer 2

woops i meain 8 :P

Answer 3

so its just 8 times 4....???? what about the differentiation??

Answer 4

Good. Now, what is the slope of the line tangent to \((8,f(8))\)? That is \(h'(6)\).

Answer 5

a bit confused...

Answer 6

Sorry. All right, so you know that the derivative at a point is the slope of the line tangent to it, right?

Answer 7

ya

Answer 8

So the derivative of \(h(x)\) at 6 (or \(h'(6)\)) is the slope of the line tangent to \(h(x)\) at \(x = 6\).

Answer 9

Now, the question is, where exactly is \(h(6)\)? We are given that \(h(x) = f(g(x))\), so \(h(6) = f(g(6))\).

Answer 10

\(f(\color{blue}{g(6)}) = f(8)\). So, go to the graph of f(x) at \(x = 8\).

Answer 11

Do you follow?

Answer 12

ya....... but the y value is not a whole number........

Answer 13

That is no problem at all! The real problem is to find the slope of the line tangent to it. But that point itself lies on a line.

Answer 14

The line tangent to a line is the line itself!

Answer 15

so i just have to find the slope of that part of the line?????

Answer 16

Exactly!

Answer 17

from f(7) to f(10)??

Answer 18

so its 4/3?????

Answer 19

!!!!!

Answer 20

whoops, no - that is not the answer