(a) Graph f(x) = 12 x2 and g(x) = f(x)+3 on thesame set of axes. What can you say about

Chapter 2, Problem 32

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(a) Graph f(x) = 12 x2 and g(x) = f(x)+3 on thesame set of axes. What can you say about the slopesof the tangent lines to the two graphs at the pointx = 0? x = 2? Any point x = x0?(b) Explain why adding a constant value, C, to any functiondoes not change the value of the slope of itsgraph at any point. [Hint: Let g(x) = f(x) + C,and calculate the difference quotients for f and g.]

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