Science:Math Exam Resources/Courses/MATH102/December 2011/Question 04 (iv)

MATH102 December 2011

  •  Q1 (a) i  •  Q1 (a) ii  •  Q1 (b) i  •  Q1 (b) ii  •  Q1 (b) iii  •  Q1 (c)  •  Q2 (a) i  •  Q2 (a) ii  •  Q2 (a) iii  •  Q2 (b) i  •  Q2 (b) ii  •  Q2 (b) iii  •  Q2 (c)  •  Q3  •  Q4 (i)  •  Q4 (ii)  •  Q4 (iii)  •  Q4 (iv)  •  Q4 (v)  •  Q4 (vi)  •  Q5  •  Q6  •  Q7 (i)  •  Q7 (ii)  •  Q7 (iii)  •  Q8 (i)  •  Q8 (ii)  •  Q8 (iii)  •  Q9  •  

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Question 04 (iv)
Consider the function $f(x)={\frac {1}{4}}x^{4}-2x^{3}+{\frac {9}{2}}x^{2}.$ iv) Determine the interval(s) for which f(x) is increasing and decreasing, respectively.

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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!

Hint
This was partially if not completely solved two problems ago. Use the derivative and make a sign chart.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. In part ii) of this question we obtained the sign table of the derivative: $\displaystyle 0$ $\displaystyle 3$ $\displaystyle x$ $\displaystyle -$ $\displaystyle 0$ $\displaystyle +$ $\displaystyle +$  $\displaystyle (x-3)^{2}$ $\displaystyle +$ $\displaystyle +$ $\displaystyle 0$ $\displaystyle +$  $\displaystyle f'(x)$ $\displaystyle -$ $\displaystyle 0$ $\displaystyle +$ $\displaystyle 0$ $\displaystyle +$  $\displaystyle f(x)$ $\displaystyle \searrow$ $\displaystyle \nearrow$ $\displaystyle \nearrow$ And we see there that the function is decreasing on the interval (-∞,0) and increasing on the intervals (0,3) and (3,+∞).

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