# Derivative applications

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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

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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))

At x = a, f(a) = a ln a

At x = b, f(b) = b ln ...

#### Solution Summary

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

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