1.6 Differentiation

The height of a biological culture, $H (t)$ millimetres, is observed over time $t\,$ hours for $t > 0$ .

Given that

$H′(t)=10t14+kt2−4\displaystyle H'(t) = 10t^{\frac{1}{4}} + \frac{k}{t^2} - 4$ , where $k\,$ is a constant
$H^{''} (t) = 0$ when $t = 16$

Determine the value of $k$ .

[3]

Given also that

Find an expression for $H (t)$ , giving each term in simplest form.

[4]

1.6 Differentiation Questions

The height of a biological culture, $H (t)$ millimetres, is observed over time $t\,$ hours for $t > 0$ .

Given that

$H′(t)=10t14+kt2−4\displaystyle H'(t) = 10t^{\frac{1}{4}} + \frac{k}{t^2} - 4$ , where $k\,$ is a constant
$H^{''} (t) = 0$ when $t = 16$

Determine the value of $k$ .

[3]

Given also that

Find an expression for $H (t)$ , giving each term in simplest form.

[4]