A model for the net capital, $C$ , of a tech startup (in millions of pounds) after $t$ years is given by

C(t) = 3t^4 - 16t^3

The function has exactly two stationary points, at $t = 0$ and $t = 4$ .

(i) Find $C^{''} (t)$ .

(a) (ii) Determine the nature of the stationary points. Fully justify your answer.

State the range of values of $t$ for which the capital $C (t)$ is an increasing function.

A revised model, $K$ , is proposed for the same startup such that

K(t) = 3t^4 + 16t^3

A model for the net capital, $C$ , of a tech startup (in millions of pounds) after $t$ years is given by

C(t) = 3t^4 - 16t^3

The function has exactly two stationary points, at $t = 0$ and $t = 4$ .

(i) Find $C^{''} (t)$ .

(a) (ii) Determine the nature of the stationary points. Fully justify your answer.

State the range of values of $t$ for which the capital $C (t)$ is an increasing function.

A revised model, $K$ , is proposed for the same startup such that

K(t) = 3t^4 + 16t^3

1.6 Differentiation

1.6 Differentiation Questions