1.9.17 Concavity and the second derivative (A-level only)

The pressure $P$ (in pascals) within a reaction vessel varies with time $t$ (in seconds) according to the function

P(t) = t^3 - ct^2 + 3t - 8

where $c\,$ is a positive constant.

Find, in simplest form, (i) $P^{'} (t)$ (ii) $P^{''} (t)$

[2]

The curve with equation $y = P^{'} (t)$ intersects the curve with equation $y = P^{''} (t)$ at the points $A\,$ and $B$ .

Given that the $t$ -coordinate of $A\,$ is 5,

find the value of $c$ .

[2]

Hence find the coordinates of $B$ .

[3]

1.9.17 Concavity and the second derivative (A-level only) Questions