How are the slopes of linearization functions related

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Reference no: EM13966678

Suppose that f(x) is a differentiable function and assume that g(x) is the inverse function of f(x). Let L1(x) be the linearization of f(x) at x=a and let L2(x) be the linearization of g(x) at x=b where b=f(a).

a) Write the formulas for L1(x) and L2(x).

b) How are the slopes of L1(x) and L2(x) related?

c) If the graph of L1(x) is not a horizontal line, then show that L2(x) is the inverse funciton of L1(x)

d) if f'(a) ≠ 1, -1 , explain why the graphs of L1(x) and L2(x) intersect on the line given by y=x

Reference no: EM13966678

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