NBT Mathematics Functions and Calculus 3

Question 1

What is the derivative of f(x) = sin(x)?

Accepted Answer

cos(x)

Answer

By the standard trigonometric derivative rule, d/dx[sin(x)] = cos(x).

Question 2

The area under f(x) = 2x from x = 0 to x = 3 is:

Accepted Answer

9

Answer

∫₀³ 2x dx = [x²]₀³ = 9 − 0 = 9.

Question 3

If f(x) = eˣ, then f′(x) equals:

Accepted Answer

eˣ

Answer

The exponential function eˣ is its own derivative: d/dx[eˣ] = eˣ.

Question 4

A function f(x) is concave down on an interval when:

Accepted Answer

f″(x) < 0

Answer

A negative second derivative means the rate of change is decreasing, indicating the graph curves downward (concave down).

Question 5

The y-intercept of f(x) = 3x² − 5x + 2 is:

Accepted Answer

2

Answer

The y-intercept is found by setting x = 0: f(0) = 0 − 0 + 2 = 2.

National Benchmark Test (NBT) Practice Test