In the figure, f is continuous on [a, b], f has minimum value at a certain point. Which is this point?

1. A
2. B
3. C
4. A and B

Ans: c

The condition for the function y = f(x) to have local minimum values at a point are

Ans: d

The function f(x) = x² - 2x increasing for

1. x ≤ 1
2. x ≥ 1
3. x < 1
4. x > 1

Ans: b

In which interval is the function f(x) = 4x - 2x² increasing?

1. (-∞, 1)
2. (1, ∞)
3. (2, ∞)
4. (3, ∞)

Ans: b

The functions f(x) is increasing on a domain D if

1. f'(x) < 0 for all x in D
2. f'(x) = 0 for all x in D
3. f'(x) > 0 for all x in D
4. f'(x) doesn't exist for all x in D

Ans: c

The function f (x) = x² - 2x is decreasing at

1. x ≥ 1
2. x ≤ 1
3. x > 1
4. x < 1

Ans: d

The total cost functions C(x) = x² + 2x and the revenue function R(x) = 5x. Which of the following the marginal profit function?

1. x² - 3x
2. 3x - x²
3. 3 - 2x
4. 2x - 3

Ans: c

The point of inflection of the function y = x⁴ is

1. 0
2. 1
3. -1
4. No point of inflection

Ans: d