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Find dy/dx and also d^2y/dx^2. For which values of t is the curve concave upward? 0 votesFind dy/dx and d^2y/dx^2. For which values of t is the curve concave upward?x = 2 sin t, y = 3 cos t, 0 parametric-equationsfirst-and-second-derivativesconcave-upwardaskedFeb 2, 2015in CALCULUSby anonymous
Please log in or register to add a comment. Please log in or register to answer this question. 1 Answer 0 votes

Step 1:

The curve is

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and also
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.

You are watching: For which values of t is the curve concave upward?

Consider

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.

Differentiate with respect to

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.

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Consider

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Differentiate with respect to

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.

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Find

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.

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Find

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.

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Step 2:

Consider

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.

For concave upwards

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Multiplying by negative sign will reverse the inehigh quality.

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*

Secant value is negative in Second and also 3rd quadrant that is

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.

Hence, the curve is concave upwards in

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.

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Solution:

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,
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and

The curve is concave upwards in

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.

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