Please help me with this derivative graph question!!!! AP Calc?

Question

This is the link of the problem:
http://s141.photobucket.com/albums/r77/rocketllamafootie/?action=view¤t=scan0011.jpg

Answer 1

The derivative of the function y = 1/x² is a function y‘ = -2/x³. That is the slope of the tangent line.

b)

PQ / QR = 2/w³
QR = PQ * (w³/2) = (1/w²) * (w³/2) = w/2
k = w + QR = (3/2) * w

a)

k(3) = (3/2) * 3 = 4.5

c)

dw/dt = 7
dk/dt = (3/2) * dw/dt = (3/2) * 7 = 10.5
That is the rate of change of k always, and therefore also when w=5.

d)

a – area of ΔPQR
a = (1/2) * (1/w²) * (w/2) = (1/4) * (1/w)
da/dt = -(1/4) * (1/w²) * dw/dt = -(7/4) * (1/w²)
The area of the triangle is decreasing.
When w=5 the rate of change of the area is
-(7/4) * (1/5²) = -7/100 = -0.07

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