Consider the following parametric curve. Answer parts a and b. x = 4t, y = t^5:

Question

Consider the following parametric curve. Answer parts a and b. x = 4t, y = t^5: t =-2 a Determine dy/dx in terms of t and evaluate it at the given value of t dy/dx = Select the correct choice below and, if necessary, fill in the answer box within your choice. The value of dy/dx at t = -2 is (Simplify your answer.) The value of dy/dx at t = -2 is undefined. b. Make a sketch of the curve showing the tangent line at the point corresponding to the given value of t, in each graph below, the blue dotted line is the tangent line and the red line is the curve. Choose the correct graph below.

Explanation / Answer

From the given question,

x=4t, y=t5 at t=-2

dx/dt= 4

dy/dt= 5t4

dy/dx= (dy/dt)/ (dx/dt)

=(5t4)/4

dy/dx= 5t4/4

at t=-2, dy/dx= 5(-2)4/4= 20

dy/dx at t =-2 is 20

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