Mathematics 9709 · AS & A Level · Differentiation

Differentiation — practice question

(i)[6]

At the point $A$, the tangent to the curve $y = x^3 - 9x^2 + 24x - 12$ is parallel to the line $y = 2 - 3x$. Find the equation of the tangent at $A$.

(ii)[2]

The function $f$ is given by $f(x) = x^3 - 9x^2 + 24x - 12$ for $x > k$, where $k$ is a constant. Find the smallest value of $k$ for $f$ to be an increasing function.

(b(ii))[2]

The function $f$ is defined by $f(x) = x^3 - 9x^2 + 24x - 12$ for $x > k$, with $k$ a constant. Find the least value of $k$ that makes $f$ increasing.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Differentiate correctly to obtain $\frac{dy}{dx}=3x^2-18x+24$.

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