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First Derivative Test for Local Maximum

Let the equat...

Question

Let the equation of a curve be x=a(theta+sintheta),y=a(1-costheta). If theta changes at a constant rate k then the rate of change of the slope of the tangent to the curve at theta=/3 is

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x = a (θ + sin θ)

y = a (1 - cos θ)

θ

k

θ = \frac{π}{2}

x = {sin}^{3} θ

y = a c o s^{3} θ

θ = \frac{π}{4}

x = 1 - cos θ

y = θ - sin θ

θ = \frac{π}{2}

m_{1}

P

y = x^{3} .

P

Q .

Q

m_{2}

m_{2} = k m_{1},

k

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