Gaokao Exam Gaokao Mathematics: Functions and Calculus 7

Question 1

If f(x) = x² and the tangent at point P has slope 4, find the coordinates of P.

Accepted Answer

(2, 4)

Answer

(4, 16)

Answer

(1, 1)

Answer

(2, 2)

Question 2

Evaluate ∫₋₁¹ (x³ + x) dx.

Accepted Answer

0

Answer

2

Answer

4/3

Answer

-2

Question 3

The function f(x) = e^(2x) - 2e^x + 1. The minimum value of f on ℝ is:

Accepted Answer

0

Answer

-1

Answer

1

Answer

e

Question 4

If f''(a) = 0 and f'''(a) ≠ 0, then x = a is:

Accepted Answer

An inflection point

Answer

A local maximum

Answer

A local minimum

Answer

A saddle point

Question 5

Let f(x) = x^(1/3). Find f'(8).

Accepted Answer

1/12

Answer

1/6

Answer

1/3

Answer

2

Question 6

If ∫₀^a x dx = 8, find a.

Accepted Answer

4

Answer

2

Answer

8

Answer

16

Question 7

For f(x) = ln(x) - x, identify the correct statement.

Accepted Answer

f has a global maximum at x = 1

Answer

f is increasing on its entire domain

Answer

f has no critical points

Answer

f(1) is a local minimum