Show that the function x^3 - 6x^2 + 18x + 5 increases with x for all values of x. Find the value of the function when the rate of increase is least.

Help? dont know where to start =(

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- Aug 10th 2009, 11:32 PMduskmantleDifferentiation max/min help?
Show that the function x^3 - 6x^2 + 18x + 5 increases with x for all values of x. Find the value of the function when the rate of increase is least.

Help? dont know where to start =( - Aug 11th 2009, 12:04 AMCaptainBlack
Start by showing that the derivative of $\displaystyle f(x)=x^3 - 6x^2 + 18x + 5$ is always positive. You do this by differentiating, and showing the derivative has no real roots, and is positive at some point.

The second part requires that you find the minimum of $\displaystyle g(x)=f'(x).$

CB