Question

let s = f(t) give an object’s height, in feet, above the ground t seconds after it is thrown. after 3 seconds, the object’s height is 100 feet, and it is moving up at 14 ft/sec. fill in the blanks: (a) f( ) = (b) f( ) =

Explanation:

Step1: Recall function meaning

The function $s = f(t)$ gives height at time $t$. Given at $t = 3$ seconds, height is 100 feet, so $f(3)=100$.

Step2: Recall derivative meaning

The derivative $f^{\prime}(t)$ represents the velocity at time $t$. Given at $t = 3$ seconds, velocity is 14 ft/sec, so $f^{\prime}(3)=14$.

Answer:

(a) $f(3)=100$
(b) $f^{\prime}(3)=14$