NBT Mathematics Functions and Calculus 2

Question 1

What is the maximum value of f(x) = −2x² + 8x − 3?

Accepted Answer

5

Answer

The vertex is at x = −b/(2a) = 2; f(2) = −8 + 16 − 3 = 5.

Question 2

For f(x) = x³ − 3x, the x-values of the turning points are:

Accepted Answer

x = ±1

Answer

Setting f′(x) = 3x² − 3 = 0 gives x² = 1, so x = ±1.

Question 3

Which of the following equals ∫4x³ dx?

Accepted Answer

x⁴ + C

Answer

∫4x³ dx = 4 · x⁴/4 + C = x⁴ + C by the power rule for integration.

Question 4

The asymptotes of f(x) = 2/(x − 3) + 1 are:

Accepted Answer

x = 3 and y = 1

Answer

The vertical asymptote occurs where the denominator is zero (x = 3) and the horizontal asymptote is the constant being added (y = 1).

Question 5

The average rate of change of f(x) = x² from x = 1 to x = 3 is:

Accepted Answer

4

Answer

[f(3) − f(1)] / (3 − 1) = (9 − 1) / 2 = 8/2 = 4.

National Benchmark Test (NBT) Practice Test