Increasing & Decreasing Function

What is the condition for a function f(x) to be decreasing?

If f(x) = x^2 - 2x, then f(x) is increasing for which value of x?

A function f(x) is said to be monotonic on an interval (a, b) if it is either:

If f'(x) = 2(x - 1), then f(x) is decreasing for which value of x?

What is the condition for a function f(x) to be increasing?

Let f(x) = 2x^3 - 5x^2 + 3x + 1. Which of the following intervals is the function strictly increasing?

Consider the function f(x) = x^2 - 4x + 3. Which of the following statements is true about the function?

Let f(x) = 3x^4 - 4x^3 + 2x^2 + 1. Which of the following intervals is the function strictly decreasing?

Consider the function f(x) = e^x(1 - x). Which of the following intervals is the function strictly increasing?

Let f(x) = x^3 - 6x^2 + 9x + 2. Which of the following statements is true about the function?

What is the necessary condition for a function f(x) to be increasing on an interval (a, b)?

If f'(x) < 0 for all x ∈ (a, b), what can be concluded about the function f(x) on the interval (a, b)?

What is the sufficient condition for a function f(x) to be increasing on an open interval (a, b)?

Let f(x) be a differentiable function on an open interval (a, b). If f'(x) > 0 for all x ∈ (a, b), what can be concluded about the function f(x)?

What is the graphical analysis interpretation of f'(x) > 0 for all x ∈ (a, b)?

A function f(x) is increasing on an interval (a, b) if its derivative f'(x) is:

What is the condition for a function f(x) to be monotonic on an interval (a, b)?

If a function f(x) is differentiable on an open interval (a, b) and its derivative f'(x) = 0 for all x ∈ (a, b), then what can be concluded about the function f(x)?

Let f(x) = x^3 - 3x^2 + 2x. Find the intervals on which the function is increasing?

If a function f(x) is increasing on an interval (a, b) and its derivative f'(x) is continuous on (a, b), then what can be concluded about the function f(x)?

If f'(x) ≥ 0 for all x ∈ (a, b), what can be concluded about the function f(x) on the interval (a, b)?

Let f(x) be a differentiable function on an open interval (a, b). If f'(c) > 0 for some c ∈ (a, b), what can be concluded about the function f(x)?

Let f(x) be a strictly increasing function on an interval [a, b]. What can be concluded about the inverse function f^-1?

Consider the function f(x) = x^2 - 4x + 3. What can be concluded about the function f(x) on the interval [0, 2]?

Let f(x) be a continuous function on an interval [a, b]. What is the necessary condition for f(x) to be monotonically increasing on the interval [a, b]?

What is the condition for a function f(x) to be monotonically increasing in a defined interval?

If f(x) = x^2 - 4x + 3, what can be concluded about the function?

What is the condition for a function f(x) to be monotonically decreasing in a defined interval?

If f(x) is a differentiable function on an open interval (a, b), what can be concluded about the function if f'(x) > 0 for all x ∈ (a, b)?

What is the graphical analysis interpretation of f'(x) > 0 for all x ∈ (a, b)?