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

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 ${\displaystyle p}$

 Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint.