IB Calculus Problem 10
A function \(f\) is defined for \(-4 \leq x \leq 3\).
The graph of \(f\) is shown below.
The figure is not to scale.
The graph has a local maximum at \(x = 0\) and local minima at \(x = -3\) and \(x = 2\).
Write down the x-intercepts of the graph of the derivative function, \(f^\prime\).
Write down all values of \(x\) for which \(f^\prime(x)\) is positive.
At point \(D\) on the graph of \(f\), the x-coordinate is \(-0.5\).
Explain why \(f^{\prime\prime}(x) < 0\) at \(D\).