If an object is dropped from a high cliff or a tall building, then the distance it has fallen after t seconds is given by the function $f ( t ) = 16 t ^ { 2 }$ Find its average speed (average rate of change) over the interval between $t = c \text { and } t = c + h$
A) $- 16 h$
B) $32 c + 16$
C) $32 c - h$
D) $16 c - h$
E) none of these

Question

Quizplus · Accepted Answer

The average speed (average rate of change) over the interval from $t = c$ to $t = c + h$ is calculated using the formula for the average rate of change: $\frac{f(c+h) - f(c)}{h}$. Substituting $f(t) = 16t^2$, we get $\frac{16(c+h)^2 - 16c^2}{h}$. Simplifying this expression does not match any of the given options exactly, indicating that the correct answer is not listed among the options provided.

If an Object Is Dropped from a High Cliff or a Tall