Answer is : D. (0, 3/2) ∪ (3, ∞)
⇒ f(x) = [x(x - 3)]2
⇒ f'(x) = 2[x(x - 3)] = 0
⇒ x = 3 and x = 3/2
When x > 3/2 the function is increasing
x < 3 function is increasing.
⇒ (0, 3/2) ∪ (3, ∞) Function is increasing.
Is a function increasing if derivative is 0?
If the derivative happens to be zero then the function is constant, neither increasing nor decreasing. Example 1: In the given graph of the function f(x), determine the interval(s) where the function is increasing, decreasing, or constant.
Is X² an increasing function?
So your function f(x)=x2 defined on the domain [0,∞) is strictly increasing.
When can we say that a function is strictly increasing?
Strictly Increasing Function - A function f(x) is said to be strictly increasing on an interval I if for any two numbers x and y in I such that x < y, we have f(x) < f(y).