The derivative f’(x) is always positive for all x in the interval (0, 2).
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If the derivative f'(x) is always positive for all x in the interval (0, 2), then the function f(x) is increasing on the interval (0, 2).
This means that as x increases from 0 to 2, the values of f(x) also increase. In other words, the slope of the tangent line to the graph of f(x) is always positive on the interval (0, 2).
Here's an example to illustrate this concept: Let's say f(x) = x^2. Then, f'(x) = 2x. Notice that f'(x) is always positive for x > 0. This means that the function f(x) is increasing on the interval (0, 2), because as x increases from 0 to 2, the values of f(x) also increase.
So, if the given statement is true, then the function f(x) is increasing on the interval (0, 2).
Answers & Comments
Answer:
The derivative f’(x) is always positive for all x in the interval (0, 2).
___________________________
If the derivative f'(x) is always positive for all x in the interval (0, 2), then the function f(x) is increasing on the interval (0, 2).
This means that as x increases from 0 to 2, the values of f(x) also increase. In other words, the slope of the tangent line to the graph of f(x) is always positive on the interval (0, 2).
Here's an example to illustrate this concept: Let's say f(x) = x^2. Then, f'(x) = 2x. Notice that f'(x) is always positive for x > 0. This means that the function f(x) is increasing on the interval (0, 2), because as x increases from 0 to 2, the values of f(x) also increase.
So, if the given statement is true, then the function f(x) is increasing on the interval (0, 2).