Limits, differentiation, related rates, integration, trig integrals, etc.

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 $w$ is 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 $w$ is increasing at the constant rate of 7 units per second. When $w = 5$, what is the rate of change of the area of triangle $PQR$ with respect to time? Determine whether the area is increasing or decreasing at this instant.

Please help on any and/or all of these that you can, I'd very much appreciate it! And for those of you who might ask me to show my process of thought, I honestly don't even know where to start; I'm so confused.
burnbird16

Posts: 47
Joined: Sat May 22, 2010 1:29 am

Hint: Tangents have the same slope as the line at that point.

stapel_eliz

Posts: 1729
Joined: Mon Dec 08, 2008 4:22 pm

### Re: POW About Differentiation, etc.

Yes, thank you, I got that and it helped me solve all the way through.
burnbird16

Posts: 47
Joined: Sat May 22, 2010 1:29 am