## Exam-Style Question on Differentiation## A mathematics exam-style question with a worked solution that can be revealed gradually |

Question id: 27. This question is similar to one that appeared on an IB Studies paper in 2012. The use of a calculator is allowed.

Consider the function \(f(x)=6 - ax+\frac 3{x^2},x\neq 0\)

(a) Write down the equation of the vertical asymptote of the graph of \(y=f(x)\).

(b) Write down \(f'(x)\)

The line T is the tangent to the graph of \(y=f(x)\) at the point where \(x=1\) and it has a gradient of -8.

(c) Show that \(a=2\).

(d) Find the equation of T.

(e) Using your calculator find the coordinates of the point where the graph of \(y=f(x)\) intersects the x-axis.

(f) The line T also intersects \(f(x)\) when \(-2\le x\le 0\). Find the coordinates of this intersection.

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