Science:Math Exam Resources/Courses/MATH110/December 2011/Question 07 (c)

MATH110 December 2011

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Question 07 (c)
Let $f(x)=x^{2}-6x$ and let P be the point (4, -12). c) Find the slope of the line tangent to the curve y = ƒ(x) at the point (a, a2 - 6a).

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
What is the relationship between the derivative of a function at a point and the tangent line of a function at that point?

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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. First we take the derivative of the function. $\displaystyle f'(x)=2x-6$ To find the slope of the tangent line at the point (a, a2 - 6a), we simply need to plug the value x = a into the derivative. This gives: $\displaystyle f'(a)=2a-6$ So the slope of the tangent line is 2a - 6.

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