Hello
Let f(x)=1/x²
f'(x)=-2/x^3
Equation of tangent line to the graph at point P is
y=f'(w) (x-w) + f(w)
Tangent line is crossing x axis at (k,0) such as
In the figure above, line L is tangent to the graph of y=1/x^2 at point P, with coordinates (w, 1/w^2) where w>0. Point Q has coordinates (w,0). Line L crosses the x axis at the point R, with coordinates (k,0)
a)Find the value of k when w=3
b) for all w>0 find k in terms of w.
c) Suppose that w in increasing at the constant rate of 7 units per second. When w=5, what is the rate of change of k with respect to time?
d) Suppose that w increasing at the constant rate of 7 units per second. When w=5 what is the rate of change of the area of PQR with respect to time?