# parametric equation and maxmium/minimum problem

• Mar 23rd 2011, 01:25 PM
age
parametric equation and maxmium/minimum problem
could u help me with these?

James blowing machine blows spherical bubbles whose surface area ,S, increases at the rate of 25cm^2/s. What is the rate the of increase of the radius,r, when the radius is 5cm?

I ended up with 0.199cm/s

and...

find maximum,minimum or point of inflection
f(x)=x^3-3x+2
give the values of x which are concave down

i got (-1,4) as maximum and (1,0) as minimum unsure about concave bit =S

is this correct?
2)3sqrr(2x-1)
2/3(2x-1)^2/3

• Mar 23rd 2011, 03:37 PM
emakarov
Quote:

James blowing machine blows spherical bubbles whose surface area ,S, increases at the rate of 25cm^2/s. What is the rate the of increase of the radius,r, when the radius is 5cm?

I ended up with 0.199cm/s
Yes, $\displaystyle S(t)=4\pi r^2(t)$, so $\displaystyle 8\pi r(t)r'(t)=25$, from where $\displaystyle r'(t)=5/(8\pi)\approx 0.199$ when $\displaystyle r(t)=5$.

Quote:

find maximum,minimum or point of inflection
f(x)=x^3-3x+2
give the values of x which are concave down

i got (-1,4) as maximum and (1,0) as minimum unsure about concave bit
I agree with maximum and minimum. The inflection point is (0, 2) because the second derivative changes sign from negative to positive. The curve is concave down when the second derivative is negative.

Quote:

is this correct?
2)3sqrr(2x-1)
2/3(2x-1)^2/3
I am not sure I understand the question.
• Mar 23rd 2011, 04:23 PM
age
thank you very much for your feedback :)