quiz5Bsol - Solutions to Quiz 5B www.math.u.edu/harringt 1...

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Solutions to Quiz 5B www.math.ufl.edu/˜harringt February 25, 2008 1. Find the equation of the tangent line to the curve f ( x ) = x 3 - 2 x +2 at the point (0 , - 1). First we need to find f ( x ) to compute the slope of the tangent line. Here we will use the quotient rule. f ( x ) = ( x + 2) d dx ( x 3 - 2) - ( x 3 - 2) d dx ( x + 2) ( x + 2) 2 = ( x + 2) * (3 x 2 ) - ( x 3 - 2) * 1 ( x + 2) 2 Next, we need to find the slope of the tangent line at (0 , - 1), so the slope is m = f (0) = (0 + 2) * (0 2 ) - (0 3 - 2) * 1 (0 + 2) 2 = 2 4 = 1 2 Recall that y = m * x + b where b is the y -intercept. Since the function goes through (0,-1) we already know that b = - 1. Thus, the line is y = 1 / 2 x - 1. NOTE: Notice that I did not waste time in reducing or rewriting f ( x ). Once I found the found the derivative, I stopped and plugged in the value that I needed. Only reduce or simplify when it is asked of you or
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