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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

Step 1:

The curve is

and also
.

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

Consider

.

Differentiate with respect to

.

Consider

Differentiate with respect to

.

Find

.

Find

.

Step 2:

Consider

.

For concave upwards

Multiplying by negative sign will reverse the inehigh quality.

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

.

Hence, the curve is concave upwards in

.

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Solution:

,
and

The curve is concave upwards in

.