# Math Help - derivative/tangent line words!

1. ## derivative/tangent line words!

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?

2. 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)

$y=-\frac{2}{w^3}x+\frac{3}{w^2}$

Tangent line is crossing x axis at (k,0) such as
$0=-\frac{2}{w^3}k+\frac{3}{w^2}$

$k=\frac{3w}{2}$