1. ## calc function question

The function f has a relative maximum value of 3 at x=1, as shown in the figure above. If h(x)=x^2f(x), then h'(1)=

It gives me a graph that i drew below..Do I need to find the function equation of f(x) first? If so how would I do that? thanks for the help.

2. Originally Posted by jst706
The function f has a relative maximum value of 3 at x=1, as shown in the figure above. If h(x)=x^2f(x), then h'(1)=

It gives me a graph that i drew below..Do I need to find the function equation of f(x) first? If so how would I do that? thanks for the help.
Hello,

I assume that the function h is: $\displaystyle h(x) = x^2 \cdot f(x)$. If so use the product rule to calculate the derivative:

$\displaystyle h'(x) = f(x) \cdot 2x + x^2 \cdot f'(x)$

f(1) = 3
f'(1) = 0
Substitute these values into the equation of the drivative:

$\displaystyle h'(1) = 3 \cdot 2 + 1^2 \cdot 0 = 6$

3. thanks a lot...very well explained...one quick question though..f'(1)=0 because the derivative of three is 0 correct?

4. Originally Posted by jst706
thanks a lot...very well explained...one quick question though..f'(1)=0 because the derivative of three is 0 correct?
Hi,

as you may know a function has an extremum (maximum or minimum) if the first derivative is zero. Thus you know if a function has a maximum at x = 1 the drivative at x = 1 must be zero.