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Numerade Educator

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Problem 50 Medium Difficulty

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

Answer

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

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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