applications of differentions

[jlcowgill]

questions is find the interval of increasing and decreasing

H(x) = (x^2-1)^3

 

H'(x) = 6x(x^2 - 1)^2

is my crital numbers x = 0, x= sq root 1, x= sq root of -1

when i am plugging them in numbers i plug them in to the deritive example

-2 it = a negitive number decreasing ,-.5 it is decreasing, .5 increasing , 2 increasing

 

them for concave up or down i do the same thing and get H"(x) = 12x(x^2-1) are these concepts correct?

 

thanks

joe

[Pat Says]

If your first derivative is negative then your equation's slope is negative; if your second derivative is negative then your equation is concave down and vice-versa. Do you know what a sign chart is? This will give you a good representation of how your equation will look when graphed. For all intents and purposes the critical points on the 1st derivative will mean the graph has a slope of zero or a vertical slope. For the 2nd derivative the critical point will mean it has inflection or nothing at all (has to change sign in order for it to be inflection).