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### SolutionKeyQuiz3

Course: MA 123, Fall 2008
School: Kentucky
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Word Count: 314

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September Quiz#3 19, 2003 Solution Key 1. Suppose the equation of the tangent line to the graph of f (x) at x = 3 is given by y = 4x 5 and that the equation of the tangent line to the graph of g(x) at x = 3 is given by y = 3x 2. Determine the equation f (x) of the tangent line to the graph of h(x) = at x = 3. (g(x))2 Solution: Since the equation of the tangent line to the graph of f (x) at x = 3 is given by y =...

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September Quiz#3 19, 2003 Solution Key 1. Suppose the equation of the tangent line to the graph of f (x) at x = 3 is given by y = 4x 5 and that the equation of the tangent line to the graph of g(x) at x = 3 is given by y = 3x 2. Determine the equation f (x) of the tangent line to the graph of h(x) = at x = 3. (g(x))2 Solution: Since the equation of the tangent line to the graph of f (x) at x = 3 is given by y = 4x 5 it follows that f (3) = 4(3) 5 = 7 and that f (3) = 4. Since the equation of the tangent line to the graph of g(x) at x = 3 is given by y = 3x 2 it follows that g(3) = 3(3) 2 = 7 and that g (3) = 3. Since we are trying to nd the equation of the tangent line to the graph of h(x) at x = 3 we need to nd a point and a slope. In particular, we need to determine (3, h(3)) (the point) and h (3) (the slope). h(3) = f (3) 7 1 = h(3) = = 2 2 (7) (g(3)) 7 3, 1 . 7 So the point (3, h(3)) is the point In order to determine h (3) we must rst determine h (x). To take the derivative of h(x) we will need to apply the quotient rule. h (x) = (g(x))2 f (x) f (x) 2(g(x))1 g (x) ((g(x))2 )2 (g(x))2 f (x) f (x) 2(g(x))1 g (x) . (g(x))4 (g(3))2 f (3) f (3) 2(g(3))1 g (3) . (g(3))4 So h (x) = In order to determine h (3) we replace x in the above expression with 3. So h (3) = 1 = h (3) = (7)2 (4) 7 2 (7)1 3 2 = . 4 (7) 49 We now know that the ...

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