TMUA Y and A Tutoring Paper 1 with Answers and Hints · Question 7

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Y and A Tutoring Paper 1 with Answers and Hints · Q7

Paper 1Algebra

Let $f(x)=2x^3-9x^2+12x$ and $g(x)=c$ , where $c$ is a real constant.

Let $m$ be the number of distinct real solutions to the equation $f(x)=g(x)$ , and let $n$ be the number of distinct real solutions to the equation $f'(x)=g'(x)$ .

What is the maximum possible value of $m+n$ ?

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