1.5.6 Polynomials and rational expressions

A specialized drone's vertical displacement from a reference altitude, $h$ (in meters), is modeled by the function

h(t) = at^3 + 3t^2 + bt - 10

where $t\,$ is the time in seconds since the drone began its descent and $a\,$ and $b\,$ are constants.

When $h (t)$ is divided by $(t - 3)$ , the remainder is 44.

Use the remainder theorem to show that

9 a + b = 9

[3]

Given also that $(t + 1)$ is a factor of $h (t)$ ,

find the value of $a\,$ and the value of $b$ .

[3]

Find $h^{'} (t)$ .

[2]

Hence find the exact coordinates of the stationary points of the curve with equation $y = h (t)$ .

[4]

1.5.6 Polynomials and rational expressions Questions