Explore BrainMass

Differentiation and critical points

1.) Differentiate these functions.

a.) (sqrt(x)+1)/(x^2)
b.) 3^x (cubedroot of (x+5)) - ((ln(x))/sqrt(x))

2.) Consider the function f(x)= x^3- (1/2)x^2 - 4x + 5

a.) find all critical points of 'f '.
b.) Does 'f ' have an inflection point? Explain your answer.
c.) Determine the intervals on which 'f ' is concave up and the intervals on which 'f ' is concave down.
d.) Find the values of all local minima and local maxima of 'f '. Explain why each value you find is a minimum or a maximum.
e.) Find values of the global maximum and global minimum of 'f' over the interval [-20,20]

Solution Summary

This provides examples of differentiating functions and working with critical points of a function.