Question

1. suppose ( h(t) = -5t^2 + 10t + 3 ) is an expression giving the height of a diver above the water in meters, ( t ) seconds after the diver leaves the springboard.

a. determine the instantaneous rate of change of the diver’s height with respect to time at 2 seconds.

Explanation:

Step1: Correct variable notation

Assume \( h(t) = -5t^2 + 10t + 3 \) (replace \( x \) with \( t \) for time).

Step2: Find derivative of height

Instantaneous rate = \( h'(t) \). Use power rule: \( h'(t) = -10t + 10 \).

Step3: Substitute \( t = 2 \)

\( h'(2) = -10(2) + 10 = -20 + 10 = -10 \).

Answer:

-10 meters per second