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# Find a function $f$ such that $f'(x) = x^3$ and the line $x + y = 0$ is tangent to the graph of $f$.

## $$f(x)=\frac{1}{4} x^{4}+\frac{3}{4}$$

Derivatives

Differentiation

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##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

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### Video Transcript

we know we're trying to find the X coordinate when the derivative equals negative one There for Alexa X cubed equal to negative one we get AKs is negative one to the power of 1/3 which is negative one. Therefore, using the tangent line Why is negative x negative negative. Want which is positive one. Therefore, if after backs is 1/4 axe to the fourth proceed may get one is 1/4 times negative one Combats are acts in this context to the fourth pussy giving us 3/4 equal. See, giving us a function after box is one fork extra fourth plus three divide by four

#### Topics

Derivatives

Differentiation

Volume

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp