June 2024 Paper 2 Q10

10 f is a cubic function.

The curve \(\quad y = \mathrm{f}(x) \quad\) has

a minimum point at \((a, 0)\)

and

a maximum point at \((1, b)\)

Sketch of a cubic curve y = f(x) with a maximum point at (1, b) and a minimum point touching the x-axis at (a, 0)

Tick one box for each statement. [2 marks]

TrueFalse
The tangent to the curve at \((1, b)\) is parallel to the \(x\)-axis
There are three different values of \(x\) for which \(\quad y = 0\)
The function is increasing for \(\quad 0 \lt x \lt 1\)