QCEVault

Further applications of differentiation — Question 355

Original QCE Vault practice · 6 marks

Q355 · Practice questionTechnology-freeComplex familiar6 marks

QUESTION 355 (6 marks)

The graph of f′(x)=x2−4f^{\prime}(x)=x^2-4 is shown on the left. It is known that f(0)=1f(0)=1. Use the grid on the right for your sketch.
Left: derivative graph x squared minus 4 on [-3,3]. Right: blank Cartesian grid for a student sketch, x from -3 to 3 and y from -7 to 7.
a)
Determine and classify both stationary points of ff.
[2 marks]
b)
Determine the point of inflection of ff.
[1 mark]
c)
Sketch a possible graph of ff for −3≤x≤3-3\leq x\leq3, labelling the points found in parts a) and b).
[3 marks]
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