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(C) The height function is $h(t) = -5t^2 + 14t + 3$.To find the maximum height, we find the derivative with respect to $t$ and set it to zero: $\frac{

Vedclass · Accepted Answer

$12.8$

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(C) The height function is $h(t) = -5t^2 + 14t + 3$.To find the maximum height, we find the derivative with respect to $t$ and set it to zero: $\frac{dh}{dt} = -10t + 14$.Setting $\frac{dh}{dt} = 0$, we get $-10t + 14 = 0$, which implies $t = 1.4 	ext{ s}$.Substitute $t = 1.4$ into the height equation: $h(1.4) = 3 + 14(1.4) - 5(1.4)^2$.$h(1.4) = 3 + 19.6 - 5(1.96) = 22.6 - 9.8 = 12.8 	ext{ m}$.Thus, the maximum height is $12.8 	ext{ m}$.

$A$ ball is thrown in the air. Its height at any time $t$ is given by $h = 3 + 14t - 5t^2$. What is the maximum height it can reach?

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