1.10.3 Applications of differentiation

A potential energy function $V$ is defined for all real values of $x$ as

V(x) = x^4 + 8x^3

The function has exactly two stationary points, at $x = 0$ and $x = - 6$ .

(i) Find $V^{''} (x)$ .

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

[6]

State the range of values of $x$ for which $V(x) = x^4 + 8x^3$ is an increasing function.

[2]

A second potential function $W$ is defined for all real values of $x$ as

W(x) = x^4 - 8x^3

(i) State the single transformation which maps the graph of $V$ onto the graph of $W$ .

(ii) State the range of values of $x$ for which $W$ is an increasing function.

[3]

1.10.3 Applications of differentiation Questions