IB Maths AA SL AA 5.2 practice question

Question 1

Paper 2, calculatorMedium6 marks

The function $f$ is defined, for $x\in\mathbb R$ by

f(x)=\frac14x^4-\frac32x^2+2x.

Figure 1 shows the graph of $f'(x)=(x+2)(x-1)^2$ for $-3\leq x\leq 3$

(a)

Use Figure 1 to state the $x$ -coordinates of the stationary points of $f$ and classify each as a local maximum, a local minimum or neither. Justify your classifications using the sign of $f'(x)$ on either side.

[3]

(b)

Use Figure 1 to determine the $x$ -coordinates of the points of inflexion of $f$ Hence determine the coordinates of both points of inflexion and the gradient of $f$ at each.

[3]

More AA 5.2 Applications of differentiation questions