Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The curve given by $y = x^3 - 2x^2 + 5x$ goes through the origin.
(i)[3]

Prove that the curve has no stationary points.

(ii)[5]

With the gradient of the curve written as $m$, determine the stationary value of $m$ and state its nature.

(iii)[4]

Showing all necessary working, determine the area of the region bounded by the curve, the $x$-axis and the line $x = 6$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Differentiation gives $\frac{dy}{dx}=3x^2-4x+5$.” …

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