Help with AP Calculus AB problem relating to derivatives of inverse functions

Test Preparation AP Mathematics & Computer Science
1

<ol>
<li>f(x)=x^(5)+2x^(3)+x-1</li>
</ol>

<p>a. Find f(1) and f'(1).</p>

<p>f(1)=1^(5)+2(1)^(3)+1-1=3 </p>

<p>f'(x)=5x^(4)+6x^(2)+1
f'(1)=5(1)^(4)+6(1)^(2)+1=12</p>

<p>f(1)=3, f'(1)=12</p>

<p>b. Find f^-1(3) and (f^-1)'(3)</p>

<p>I figured since it's the inverse, f^-1(3)=1 since f(1)=3, is that correct?</p>

<p>I couldn't figure out how to find (f^-1)'(3).</p>

<p>The way my book explains how to do it is horrible and it's an even problem so the answer isn't in the back of the book.</p>

2

<p>So lets say you’re asked to find (f^-1)’(3)</p>

<p>well thats equal to 1/(f’(f^-1 (3))</p>

3

<p>Actually I ended up figuring it would be 1/12 since i thought it would be the reciprocal of f’(1) and if you do what you said to do it’s also 1/12, so I guess I was right. Thanks!</p>