Determine the second derivative of $f(x)=-5x^3+17x^2-5x+3$.

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Lesson Parent: 
Chapter 14 - Second Derivatives
Problem: 

Determine the second derivative of $f(x)=-5x^3+17x^2-5x+3$.

Answer: 

$f\,''(x)=-30x+34$

Solution: 

This is a polynomial and we know how to find the derivative of a polynomial. Therefore,
\[
f\,'(x)=-15x^2+34x-5.
\]

Now $f\,'(x)$ is also a polynomial so we can find its derivative. It is
\[
f\,''(x)=-30x+34.
\]