Find the Critical Number's of the function:?

Question

A(x)= x sqrt x+3

Answer 1

To determine the critical numbers, you must find where A'(x) is equal to 0 or where A'(x) is undefined.

A'(x) = sqrt(x) + x(1/2)(1/sqrt(x))
A'(x) = sqrt(x) + x / [2(sqrt(x)]

Now, put it under a common denominator.

A'(x) = (2x + x)/[2(sqrt(x)]
A'(x) = (3/2) [x/sqrt(x)]
A'(x) = (3/2) x^(1/2)

To find the critical number, equate this to 0
(3/2) x^(1/2) = 0
x^(1/2) = 0
Therefore, x = 0

Answer 2

it is
(x^3/2)+3
diff wrt x
(3/2)x^1/2
take this equal to zero
u get
x=0
as critical number