Question

1. an object is sent through the air. its height is modelled by the function $h(x)=-5x^{2}+3x + 65$, where $h(x)$ is the height of the object in metres and $x$ is the time in seconds. estimate the instantaneous rate of change in the objects height at 3 s.

Explanation:

Step1: Find the derivative of $h(x)$

The derivative of $h(x)=- 5x^{2}+3x + 65$ using the power - rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$ is $h'(x)=-10x + 3$.

Step2: Evaluate $h'(x)$ at $x = 3$

Substitute $x = 3$ into $h'(x)$: $h'(3)=-10\times3+3$.
$h'(3)=-30 + 3=-27$.

Answer:

$-27$ m/s