# Exam Style Question

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

### Differentiation

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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