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A ball thrown vertically upward at time t = 0 (s) with initial velocity 80 ft/s and with initial height 96 ft has height function

A ball thrown vertically upward at time t = 0 (s) with initial velocity 80 ft/s and with initial height 96 ft has height function:

a) What is the maximum height attained by the ball?

b) When and with what impact speed does the ball hit the ground?
y(t)= -16t^2+ 80t+ 96

Find the interval on which the function is increasing and decreasing. Sketch the graph of y = f(x), and identify any local maxima and minima. Any global extrema should also be identified.

f(x)=(x-2)^2(x+3)^2

Solution Preview

[a] y' (t) = -32t + 80

and this is 0 when t = 80/32 = 2.5 s

[b] now, the ball hits the ground when - 16 t^2 + 80 t + 96 = 0
i.e. at t = 6 s.

the velocity with which the ball hits the ground is therefore y ' (6) = -- 112 ft/s

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to find the intervals, find the ...

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