# Find {eq}\displaystyle f(x). {/eq} {eq}\displaystyle f''(x) = x - 2 , \text{ when } x \geq 0. \ \ f(1) = 0, \ \ f(2) = 0. {/eq}

## Question:

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

{eq}\displaystyle f''(x) = x - 2 , \text{ when } x \geq 0. \ \ f(1) = 0, \ \ f(2) = 0. {/eq}

## Initial-Value Problem:

An initial-value problem is a type of indirect integral problem. If an initial value is given for the integrated function, this will allow us to evaluate the constant(s) of integration. The initial values given are usually values of the function evaluated at certain points.

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Given:

• {eq}\displaystyle f''(x) = x - 2 {/eq}
• {eq}\displaystyle f(1) = 0 {/eq}
• {eq}\displaystyle f(2) = 0 {/eq}

Here we have two initial...