Science:Math Exam Resources/Courses/MATH102/December 2011/Question 02 (c)

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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[hide] Question 02 (c)
Consider the function in the graph shown below. Draw a qualitatively accurate sketch of its derivative on top of it.

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!

[show] Hint
Remember that the derivative of a function is the slope of that function.

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[show] 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. To draw a qualitatively accurate sketch of the derivative of the function (i.e: $f'(x)$), we need to observe some qualitative features of the slope: (1) We notice that the slope of the function is zero (i.e: function has a horizontal tangent line) at $x=-1$ and $x=1$. (i.e: $f'(x)=0$ at $x=-1$ and $x=1$) (2) We notice the function has positive slope on $(-1,1)$ (i.e: $f'(x)>0$ on $(-1,1)$) (3) We notice the function has negative slope on $(-3,-1)\cup (1,3)$ (i.e: $f'(x)<0$ on $(-3,-1)\cup (1,3)$). So we need to sketch a curve for $f'(x)$ that the properties described in points (1)-(3). Such a curve is plotted in black below.