Science:Math Exam Resources/Courses/MATH110/December 2012/Question 02 (f)

MATH110 December 2012

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Question 02 (f)
Determine whether the following statement is true or false. If it is true, provide justification. If it is false, provide a counterexample. The curve $y={\sqrt {x}}$ has no horizontal tangent lines.

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
In order for a function to have horizontal tangent lines, at some point its derivative must be equal to zero.

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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. Horizontal tangent lines occur when the derivative equals zero. The derivative of y is $y'={\frac {1}{2{\sqrt {x}}}}$ However, this derivative is never zero, because for all positive values of x (the domain of the derivative), $y'$ will be a positive number, not zero. Thus $y={\sqrt {x}}$ has no horizontal tangent lines, so the statement is true.

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