True/False: "The only critical points of the function f(x) = x1/3 are x = 0 and x = ± 1/square root of 27"

Question

True/False: "The only critical points of the function f(x) = x1/3 are x = 0 and x = ± 1/square root of 27"

Answer 1

y = x^(1/3)

y' = (1/3) x^(-2/3) = 1/(3*x^(2/3))

there are no values of x where the derivative is zero...

please repost with the correct function

Answer 2

Graph this function!

There are no maxima and minima.

There is a point of inflection at x=0.

Answer 3

I assume you mean

f(x) = x^1/3

When I plot this, I see only one critical point. When x = 0, f(x) = 0, and there is a local positive slope. For x values less than ±1, the absolute value of f(x) is greater than x, and for larger values of x, f(x) is smaller.

Nothing special happens at x = 27

Always plot thing like this to help visualize. Here is my favorite online plotting tool:

https://www.desmos.com/calculator