Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The diagram displays the curve whose equation is $y = 9\left(x^{\frac{1}{2}} - 4x^{-\frac{3}{2}}\right)$. This curve meets the $x$-axis at $A$.
(a)[2]

Determine the $x$-coordinate of $A$.

(b)[4]

Determine the equation of the tangent to the curve at $A$.

(c)[2]

State the $x$-coordinate of the maximum point on the curve.

(d)[4]

Determine the area of the region enclosed by the curve, the $x$-axis and the line $x = 9$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Set the derivative equal to zero and simplify until you have $9x^{-3/2}(x-4)=0$

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