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Emilio throws a marshmallow into the air from his balcony. The height of the marshmallow (in feet) is represented by the equation h=−16(t−14)2+49, where t is the time (in seconds) after he throws the marshmallow. What is the maximum height of the marshmallow? Enter your answer as the correct value, including units, like this: 42 meters Be sure to use the correct units from the context of the problem.

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mathstudent55

Answer:

49 ft

Step-by-step explanation:

h=−16(t−14)^2+49

The path of the marshmallow is an inverted parabola. It has symmetry with respect to its vertical axis.

We take the derivative of the height function.

dh/dt = -32(t - 14)

dh/dt = -32t + 448

We set the derivative equal to zero ti find the value of t corresponding to a maximum value of h.

-32t + 448 = 0

-32t = -448

t = 14

Maximum height occurs at t = 14 seconds.

h=−16(t−14)^2+49

t = 14

h=−16(14−14)^2+49

h = 49

Maximum height is 49 feet.

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