Function Problem

[Jason76]

\(\displaystyle f(x) = 4x^{2} + 2\) and \(\displaystyle g(x) = 9x^{3} + 3\) Given \(\displaystyle h(x) = f(g(x))\) What is \(\displaystyle h'(3)\)

What is the first step? Multiply the two functions?

 

[pka]

\(\displaystyle f(x) = 4x^{2} + 2\) and \(\displaystyle g(x) = 9x^{3} + 3\) Given \(\displaystyle h(x) = f(g(x))\) What is \(\displaystyle h'(3)\) What is the first step? Multiply the two functions?

If \(\displaystyle h(x) = f(g(x))\) that is not multiplication it is function composition.

So use chain rule: \(\displaystyle h'(x) = f'(g(x))g'(x)\),
Now you need \(\displaystyle g(3)=?\) to get \(\displaystyle f'(g(3))=?\) and finally you need \(\displaystyle g'(3)=?\).

Then multiply.

 

[DrPhil]

\(\displaystyle f(x) = 4x^{2} + 2\) and \(\displaystyle g(x) = 9x^{3} + 3\) Given \(\displaystyle h(x) = f(g(x))\) What is \(\displaystyle h'(3)\)

What is the first step? Multiply the two functions?

NO.

You "could" expand h(x) by substituting the expression for g(x) wherever "x" occurs in f(x) .. BUT I would not attempt that! As I said somewhere,

1) differentiate f[g(x)] using the chain rule

2) What is g(x=3)?

3) Where do you need to know the derivatives of f(x) and g(x)?

 

[Jason76]

Basically, you would plug in g(x) into f (into the x value contained in f(x)) (I looked it up on some free videos). Then you would take the derivative of this final answer and plug in 30. Is that right?

 

[Deleted member 4993]

Basically, you would plug in g(x) into f (into the x value contained in f(x)) (I looked it up on some free videos). Then you would take the derivative of this final answer and plug in 30. Is that right?

Instead of using words - use equations, functions and numbers. Then it will make better sense to us.

 

[DrPhil]

Basically, you would plug in g(x) into f (into the x value contained in f(x)) (I looked it up on some free videos). Then you would take the derivative of this final answer and plug in x=3. Is that right?

OK - that is NOT what I recommended, but if you can do the algebra correctly then you should get the correct answer.

Try it, and show us your steps.

Then do it our way (DrPhil and pka have both told you what to do), and compare results. Which way do you think was easier?