`g(t) = tan(2t), ((pi/6),sqrt(3))` Evaluate the second derivative of the function at the given point. Use a computer algebra system to verify your result.

Textbook Question

Chapter 2, 2.4 - Problem 94 - Calculus of a Single Variable (10th Edition, Ron Larson).
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gsarora17 | (Level 2) Associate Educator

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`g(t)=tan(2t)`

differentiating with respect to t,

`g'(t)=sec^2(2t)*2` ` `

differentiating again,

`g''(t)=2(2sec(2t))(sec(2t)tan(2t)*2)`

`g''(t)=8tan(2t)sec^2(2t)`

Now to evaluate the g''(t) at t=pi/6 , plug in the value

`g''(pi/6)=8tan(2*pi/6)sec^2(2*pi/6)`

`g''(pi/6)=8tan(pi/3)sec^2(pi/3)`

`g''(pi/6)=8*sqrt(3)*(2^2)`

`g''(pi/6)=32sqrt(3)`

Graph of g''(t)

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