Calculus Problem of the Week – Week of July 25, 2011

Sometimes easy and sometimes hard, our calculus problem of the week could come from any calculus topic. If you really want to get better at calculus, following these problems is a great way to make yourself practice! Past calculus problems of the week.

This week’s problem:
(click “see the solution” at the bottom of post to, well, see the solution.)

Suppose you know the following information about two functions:


Use this information to find [f(g(2))]'.

See the solution.

f(g(x)) is a composite function, so to find the derivative you should use the chain rule. Applying the chain rule here would give us [f(g(x))]'=f'(g(x))\cdot g'(x). Therefore [f(g(2))]'=f'(g(2))\cdot g'(2)=f'(2)g'(2)=7\cdot (-3)=-21

Notice that if it wasn’t true that g(2)=2, we wouldn’t have been able to do this since we only knew f(2).