Science:Math Exam Resources/Courses/MATH110/December 2011/Question 08 (a)
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Question 08 (a)
Let , where a and b are constant.
(a) Suppose that a ≠ 0. Find the equation of the line tangent to the curve at
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If a is different than zero, then the given curve is a polynomial of degree 7. Let
then its derivative (using the chain rule) is
and so the slope of the tangent line to this curve at the point x = b/a is
And the y coordinate of that point is which is
So using the standard equation
for a line of slope m and going through the point (x0, y0) we obtain
which you can simplify a bit and obtain
or if you compute things out
You don't need to do the last two steps during a test usually.