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    Derivative of a function

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    Let f be the function whose graph goes through point (3,6) and whose derivative is given by f'(x) = (1+e^(x))/(x^2)

    a) write the equation of the line tangent to the graph of f at x=3 and use it to approximate f(3.1)

    b) Use Euler's method, starting at x=3 with a step size of .05 to approximate f(3.1). Use f'' to explain why this approximation is less than f(3.1).

    c) Use the fact that the definite integral, from 3 to 3.1 of f '(x)dx to evaluate f(3.1)

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    Solution Summary

    This shows how to find a function with given characteristics, write the equation of the tangent line at a point, and use Euler's method.