Calculus word problem help

[salu34]

I am stuck on a couple of questions on my calculus assignment. Any help would be greatly appreciated.

1) Find the second derivative for f(x) = x+1 / x-2 (I am stuck on finding the second derivative, I can find the first one no problem)

AND

2) Helium is pumped into a spherical balloon at a constant rate of 4 cubic feet per second. How fast is the radius increasing after 1 minute? After 2 minutes? Is there any time at which the radius is increasing at a rate of 100 feet per second? Explain. V= 4/3 PIr^3

AND

3) Suppose that for a compant manufacturing calculators, the cost, revenue, and profit equations are given by C=90,000+30x R=300x - (x^2)/30 & P=R-C where the production output in 1 week is x calculators. if production is increasing at a rate of 500 calculators per week, when production output is 6,000 calculators, find the rate of increase (decrease) in: a) cost b) revenue, c) profit.

Again, any help would be much appreciated.

 

[tkhunny]

1) Let's see the first derivative.

2) Find the differentials dV and dr, assuming V and r are functons of time (t).

3) Very similar to #2. You need differentials. It's a VERY close relative of the first derivative.

 

[salu34]

for number 1) i got the first derivative to be -3/(x-2)^2 i dont know what to do, becuase i know you have to find the derivative of the top, but there is no variable there, so would it not just go to zero? also, do you need to use the product rule for the denominator?

 

[tkhunny]

You CAN use the quotient rule with no variable in the numerator, but why? The derivative of the numerator would, indeed, be zero. In this case, it's just a polynomial sort of thing. Why complicate it?

\(\displaystyle \frac{-3}{(x-2)^{2}}\;=\;-3(x-2)^{-2}\)

Are your eyes lighting up, yet?