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University of Houston

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Problem 53

Horizontal Tangent Find a function $f$ such that the graph of $f$ has a horizontal tangent at $(2,0)$ and $f^{\prime \prime}(x)=2 x$

Answer

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## Discussion

## Video Transcript

question defict they are giving us after the crime equals to Lex and yeah, crime, who is zero. And they want us to define the function. So first I have to take the into grow Would beat wall the ex We've been in too. It's purple. Uh, add one to my act Ex bear multiplied by. We'll see. So I had a crime of eggs equal x weird class. And then we have to find out what my my sea is. So I'm gonna plug in two for X and zero the zero he won't two squares or their course see would have to equal negative for So my function for prime of X equals X square minus were. And now I want to find my function. So I'm gonna take my derivative are my integral Really? Next week was the integral X squared minus four. Yeah. So X square is gonna be at one excuse. Multiply the coefficient of reciprocal minus four. We're gonna have an excellent and plus c. And now gonna be too. Zero 1/3 Q minus eight. A scene. So I get to see the equal 16. 30. So my equation for effort Eggs? No one there. Thanks. Q Minus war acts months, baby. Plus 16. Okay. Yeah,

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