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the function f(x) = ex - 2e-2x - 3/2 is graphed at right. evidently, f(x) has...

the function f(x) = ex - 2e-2x - 3/2 is graphed at right. evidently, f(x) has a zero in the interval (0,1).

(a) show that f(x) is increasing on (-infinity, infinity) (so that no other zero of f exists.)

(b) use one iteration of Newton's method to estimate the zero, starting with initial estimate x1 = 0.

(c) it appears from the graph that f(x) has an inflection point at or near the zero of f. find the exact coordinates of the inflection point and see if it does occur at the zero of f.

Math   Calculus   
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