The vertical displacement, $y\,$ millimetres, of a vibrating plate in a laboratory experiment is modelled by the function $y = f (t)$ , where

f(t) = (t - 4)(2t + 1)^2

for $\ge -1$ , where $t\,$ is the time in seconds.

The graph of $y = f (t)$ touches the $t$ -axis at the point $P\,$ and crosses the $t$ -axis at the point $Q$ .

State the coordinates of the point $P$ .

Hence show that the equation of the tangent to the curve at the point where $t = 2.5$ can be expressed in the form $y = k$ , where $k\,$ is a constant to be found.

The displacement is modified to $y = f (t + b)$ , where $b\,$ is a constant. This new curve passes through the origin $(0, 0)$ .

State the possible values of $b$ .

The vertical displacement, $y\,$ millimetres, of a vibrating plate in a laboratory experiment is modelled by the function $y = f (t)$ , where

f(t) = (t - 4)(2t + 1)^2

for $\ge -1$ , where $t\,$ is the time in seconds.

The graph of $y = f (t)$ touches the $t$ -axis at the point $P\,$ and crosses the $t$ -axis at the point $Q$ .

State the coordinates of the point $P$ .

Hence show that the equation of the tangent to the curve at the point where $t = 2.5$ can be expressed in the form $y = k$ , where $k\,$ is a constant to be found.

The displacement is modified to $y = f (t + b)$ , where $b\,$ is a constant. This new curve passes through the origin $(0, 0)$ .

State the possible values of $b$ .

1 Pure Mathematics

Question 492

Markscheme

1 Pure Mathematics

Question 492

Markscheme

1 Pure Mathematics

Question 492

1 Pure Mathematics Questions

1 Pure Mathematics

Question 492

1 Pure Mathematics Questions