Posted by **Angelina** on Thursday, March 8, 2012 at 3:21pm.

The height of a ball t seconds after it is thrown upward from a height of 6 feet and with an initial velocity of 80 feet per second is f (t) = -16t^2 + 80t + 6.

According to Rolle's Theorem, what must be the velocity at some time in the interval (2, 3)?

ft/sec?

& Find that time t?

I believe i need to take the 1st derivative which is -32t+80 equal to zero so t=-80/32? and for ft/sec plug in 2 for t? Anyhow i get wrong answers so need help!

- Math -
**Steve**, Thursday, March 8, 2012 at 5:22pm
Rolle's Theorem states that on the interval (2,3) there will be a point c where f'(c) = the slope of the chord from f(2) to f(3)

So, f(2) = 102

f(3) = 102

so, the chord has slope 0.

so, at some point c in (2,3) f'(c) = 0

f'(t) = 80 - 32t

f'(t) = where t = 80/32 = 2.5

That's what you'd expect, since parabolas are symmetric about their axis.

- Math -
**Angelina**, Thursday, March 8, 2012 at 5:40pm
THNKS :)I really appreciate your help!

## Answer this Question

## Related Questions

- Algebra - THe function h(t)=-16t^2+v0t+h0 describes the height in feet above the...
- Algebra - THe function h(t)=-16t^2+v0t+h0 describes the height in feet above the...
- Algebra - The height of a ball thrown directly up with a velocity of 40 feet per...
- math - A ball is thrown into the air with an upward velocity of 20 ft/s. Its ...
- math - If a metal ball is thrown downward with an initial velocity of 22 feet ...
- College Algebra - Flight of a Ball If a ball is thrown upward at 96 feet per ...
- math - a ball is thrown upward at 64 feet per second from the top of an 80 feet ...
- math - An object that is falling or vertically projected into the air has it ...
- calculus - A ball is thrown vertically upward with an initial velocity of 128 ...
- algebra - A ball is thrown vertically upward with an initial velocity of 128 ...