Find f.
{eq}{f}'' \left ( t \right ) = \frac{9}{\sqrt{t}} {/eq} , {eq}f \left ( 4 \right ) = 25 {/eq}, {eq}{f}'\left ( 4 \right ) = 14 {/eq}
Question:
Find f.
{eq}{f}'' \left ( t \right ) = \frac{9}{\sqrt{t}} {/eq} , {eq}f \left ( 4 \right ) = 25 {/eq}, {eq}{f}'\left ( 4 \right ) = 14 {/eq}
Antiderivatives:
From the fundamental theorem of calculus, we know that differentiation and integration are inverse processes. Since we are given the second derivative, we will need to antidifferentiate the function twice to get a solution.
Answer and Explanation: 1
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View this answerWe antidifferentiate twice to get
{eq}\begin{align*} f' &= 18t^{1/2} + C \\ f &= 12 t^{3/2} + Ct + D \end{align*} {/eq}
We apply {eq}f'(4) =...
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Chapter 8 / Lesson 12Understand what an antiderivative is and what antiderivative rules are. Use various antiderivative formulas and learn how to do antiderivatives. See the antiderivative chart for common functions and practice solving basic antiderivatives examples.