# calc 2

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The height (in feet) attained by a rocket t seconds into flight is giving by the function
h(t)= -1/3t^3 + 16t^2 + 33t + 10
When is the rocket rising?
When is the rocket decreasing?
when does it reach its maximum height above the ground?
what is the maximum height?
what is the velocity and when does maximum velocity occur?

• calc 2 -

The rocket is rising when the derivative dh/dt > 0

dh/dt = -t^2 +32t +33.

The rocket is descending when dh/dt <0.

Maximum height occurs when dh/dt = 0

Use the t when that happens to compute h(t) at maximum height

Maximum velocity occurs when the second derivative d^h/dt^2 = 0

d^2h/dt^2 = -2t + 32 = 0 @ max V

t = 16 s at maximum velocity

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