# Science:Math Exam Resources/Courses/MATH102/December 2016/Question B 06 (b)

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MATH102 December 2016
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### Question B 06 (b)

For both parts of this question, consider the function

${\displaystyle f(x)=4x^{3}-12x^{2}+9x.}$

(b) The absolute maximum of the function ${\displaystyle g_{p}(x)=f(x-p)}$ on the interval ${\displaystyle [0,2]}$ is a number that depends on ${\displaystyle p}$ and can be thought of as a function. Call that function ${\displaystyle M(p)}$ and calculate it for ${\displaystyle p\in [0,2].}$ You can use function notation in your answer (e.g. ${\displaystyle f(x)}$ instead of ${\displaystyle 4x^{3}-12x^{2}+9x}$). Hint: sketch ${\displaystyle g_{p}(x)}$ for several values of ${\displaystyle p}$

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