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University of Houston

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Problem 51

Comparing Functions Consider $f(x)=\tan ^{2} x$ and $g(x)=\sec ^{2} x .$ What do you notice about the derivatives of $f$ and $g ?$ What can you conclude about the relationship between $f$ and $g ?$

Answer

$$

f(x)=\frac{x^{3}}{3}-4 x+\frac{16}{3}

$$

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## Discussion

## Video Transcript

All right, go in. 51. We are giving effort. That's equals the annex. We're dead and G of X. We are given seek. It's weird. Ex classifying what? The right ship is between the two. I'm gonna kick, uh, derivative. Yes, I'm driving. Crime ex played for my chain rule my ex. I am. Yes. And then the derivative looked hand okay, squared eggs. And when you take the derivative again, I have to use my jail two times seeking and the derivative of seeking and speaking next, which is me to seek it. Weird X and X So I have the same function. So Beth back has seem derivative of G of X. But again, we don't know about the constant, so it's an unknown sea.