# Given : {eq}\displaystyle f''(x) = 3x - 6 {/eq}; {eq}\displaystyle \ \ \ \ f'(-3) = -5 {/eq}; {eq}\displaystyle \ \ \ \ f(-3) = -5 {/eq} Find {eq}\displaystyle f'(x) {/eq} and {eq}\displaystyle f(2) {/eq}.

## Question:

Given : {eq}\displaystyle f''(x) = 3x - 6 {/eq}; {eq}\displaystyle \ \ \ \ f'(-3) = -5 {/eq}; {eq}\displaystyle \ \ \ \ f(-3) = -5 {/eq}

Find {eq}\displaystyle f'(x) {/eq} and {eq}\displaystyle f(2) {/eq}.

## Initial Value Problem:

An initial value problem is essentially a type of integration problem. If you are given a derivative and an initial value of its integral function, you can solve the value of the constant of integration. In this way, initial value problems yield a particular solution for a given derivative instead of a general solution. Initial conditions need not be set at zero; they have to have a definite value.

Become a Study.com member to unlock this answer!

{eq}f''(x) = 3x-6, f'(-3) = -5, f(-3) = -5 {/eq}

To get from the second derivative of the function of the function, two antiderivatives will have... 