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)© BrainMass Inc. brainmass.com December 24, 2021, 4:53 pm ad1c9bdddf
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.