NSAA NSAA Mathematics - Calculus 2

Question 1

If dy/dx > 0 for all x in an interval, the function is:

Accepted Answer

Increasing

Answer

A positive first derivative indicates the function is increasing over that interval.

Question 2

The chain rule states that if y = f(g(x)), then dy/dx =

Accepted Answer

f'(g(x)) · g'(x)

Answer

The chain rule: dy/dx = f'(g(x)) · g'(x).

Question 3

Find the area under y = x² between x = 0 and x = 3.

Accepted Answer

9

Answer

∫₀³ x² dx = [x³/3]₀³ = 27/3 - 0 = 9.

Question 4

What is the derivative of e^(3x)?

Accepted Answer

3e^(3x)

Answer

Using chain rule: d/dx(e^(3x)) = 3e^(3x).

Question 5

At a maximum point, the second derivative f''(x) is:

Accepted Answer

Negative

Answer

At a local maximum, f''(x) < 0, indicating the curve is concave downward.

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