Find {eq}f {/eq}.

{eq}f''(t) = 4 - 6/t^4, f(1) = 6, f'(2) = 9, t > 0 {/eq}

Question:

Find {eq}f {/eq}.

{eq}f''(t) = 4 - 6/t^4, f(1) = 6, f'(2) = 9, t > 0 {/eq}

Initial Value Problem:

An initial value problem in calculus is a problem that provides us with a derivative and a number of conditions/initial values that will enable us to determine the constants of integration that we will pick up along the way. Note that we have the second derivative of the function we seek, and so we will need to antidifferentiate a couple times.

Answer and Explanation: 1

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We antidifferentiate the given function to find the first derivative of the function we seek:

{eq}\begin{align*} f' (t) &= \int 4 - 6t^{-4}\ dt...

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Initial Value in Calculus: Definition, Method & Example

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Chapter 11 / Lesson 13
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Learn to define the initial value problem and initial value formula. Learn how to solve initial value problems in calculus. See examples of initial value problems.


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