calculus question#3?

Question

find all of the critical numbers for f(x)=(x+7)^2/3 - 2x^2/3 . determine the intervals whee f is increasing and those where it is decreasing . determine all local extrema.

Answer 1

take the derivative of that, and find where the derivative equals zero, and where it is non differentiable. Take those points, put them on a number line, and test points in between them by plugging those numbers into the first derivative. If the number plugged into an interval is positive, the function is increasing. If negative, its decreasing on the interval. Extreme points where it goes from increasing to decreasing are maxes, and extreme points where it goes from decreasing to increasing are mins.

Answer 2

I can tell you that my critics numbers are 0 and 9.3333 according to my first derivative f´(x)= 2/{3 (x+7)^1/3} -4/{3 (2x)^1/3}
The others answers you want are ac coding to the second derivative, and I am not sure about my answers.
You can found when it decrease or increase by evaluation on the right or left of the critical numbers or obtain the second derivative and evaluate the critical numbers on the equation, if the sign (positive or negative) is positive the it decrease at that point(minimum value) and if it is negative it increase at that point (maximum value)

Answer 3

I don't understand the term critical number, but if you take the first and second derivatives, you should be able to fake it.

Answer 4

would love to help, but I am not that smart