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?

Accepted Solution

Answer:49 ftStep-by-step explanation:h=βˆ’16(tβˆ’14)^2+49The 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 = -448t = 14Maximum height occurs at t = 14 seconds.h=βˆ’16(tβˆ’14)^2+49t = 14h=βˆ’16(14βˆ’14)^2+49h = 49Maximum height is 49 feet.