Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

The diagram depicts the curve whose equation is $y = 4x^{\frac{1}{2}}$.
(i)[6]

The line $y = x + 3$ cuts the curve at $A$ and $B$. Calculate the length of $AB$.

(ii)[3]

The tangent to the curve at a point $T$ is parallel to $AB$. Determine the coordinates of $T$.

(iii)[3]

Determine the coordinates where the normal to the curve at $T$ meets the line $AB$.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Eliminate $y$ to produce an equation in $x$, for example $(x^{\frac{1}{2}})^2-4x^{\frac{1}{2}}+3=0$” …

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