Lesson of working the chain rule

Question

I was trying to help my daughter with her homework and I wrote the problem incorrectly. If anyone could help, I appreciate it.

Find the equations of the tangent and the normal line to the graph of the function at the given point g(t) = (-2 sint + 4cost)^3 at t=pi/2

I posted this yesterday and forgot the 4

Answer 1

g(t) = (-2sint + 4cost)³ g(π/2) = (-2 + 0)³ = -8

g'(t) = 3(-2sint + 4cost)²(-2cost - 4sint) g'(π/2) = 3(-2 + 0)²(0 - 4) = -48

Tangent line: y - (-8) = -48(x - π/2)

Normal line: y - (-8) = (1/48)(x - π/2)

Answer 2

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