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Derivative applications

1.) Mean Value Theorem: Let f(x)= x ln x
a.) Write an equation for the secant line AB where A= (a,f(a)) and B= (b,f(b))
b.) Write an equation for the tangent line that is parallel to the secant line AB.
2.) Approximating functions: Let f be a function with f'(x)= sinx^2 and f(0)= -1
a.) Find the linearization of f at x=0

Solution Summary

This set looks at a few examples of applying derivatives in the mean value theorem and approximating functions.