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Which of the following functions has a graph that is a line? f(x) = x f(x) = x 2 f(x) = |x| |
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Answer» The slope of the TANGENT line of a graph y=F(x) at a point x0 is given by the derivative of f at that point, that is, f'(x0) .A horizontal tangent line implies a slope of 0 , so our goal is to find the points at which the derivative f(x) evaluates to 0 .Using the quotient RULE, we find the derivative asf'(x)=ddxx2x−1 =(x−1)(ddxx2)−x2(ddx(x−1))(x−1)2 =2x(x−1)−x2(1)(x−1)2 =2x2−2x−x2(x−1)2 =x2−2x(x−1)2 =x(x−2)(x−1)2 Setting this equal to zero, we getx(x−2)(x−1)2=0 ⇒x(x−2)=0 ⇒x=0orx=2 Thus, the graph of f(x) has a horizontal tangent line at x=0 and x=2 , that is, at the points(0,0),(2,4) Step-by-step explanation: HOPE it works out for you |
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