Gaokao Exam Gaokao Mathematics: Functions and Calculus 6

Question 1

If f(x) = sin(x) - cos(x), the maximum value of f(x) is:

Accepted Answer

√2

Answer

1

Answer

2

Answer

√3

Question 2

Find the inflection point of f(x) = x³ - 3x² + x + 1.

Accepted Answer

x = 1

Answer

x = 0

Answer

x = 2

Answer

x = 3

Question 3

Which of the following pairs (f, g) satisfies f(x) + g(x) = 0 for all x?

Accepted Answer

f(x) = x², g(x) = -x²

Answer

f(x) = sin(x), g(x) = cos(x)

Answer

f(x) = eˣ, g(x) = ln(x)

Answer

f(x) = x, g(x) = |x|

Question 4

Using L'Hôpital's rule, evaluate lim_{x→0} (sin x)/x.

Accepted Answer

1

Answer

0

Answer

∞

Answer

undefined

Question 5

f(x) = x·|x|. Which statement is true?

Accepted Answer

f is differentiable everywhere with f'(0) = 0

Answer

f is not differentiable at x = 0

Answer

f is an even function

Answer

f has a local maximum at x = 0

Question 6

A particle moves along a line with velocity v(t) = 3t² - 6t m/s. The total distance traveled from t = 0 to t = 3 is:

Accepted Answer

9 m

Answer

0 m

Answer

6 m

Answer

12 m

Question 7

The solution set of f'(x) > 0 for f(x) = x³ - 3x² - 9x + 1 gives the intervals where f is increasing. These intervals are:

Accepted Answer

(-∞, -1) ∪ (3, +∞)

Answer

(-1, 3)

Answer

(-3, 1)

Answer

(-∞, -3) ∪ (1, +∞)