Calculus -- things to know to potentially boost your grade to A/B

Question 1

When is a function f(x) increasing?

Answer 1

When f’(x) > 0

Question 2

When is a function f(x) decreasing?

Answer 2

When f’(x) < 0

Question 3

In determining the nature of a stationary point of a function f(x), what kind of stationary point does f’‘(x) < 0 imply.

Answer 3

A maximum stationary point.

Question 4

In determining the nature of a stationary point of a function f(x), what kind of stationary point does f’‘(x) > 0 imply.

Answer 4

A minimum stationary point.

Question 5

How do you determine the greatest and least values of a function on a closed interval, a <= x <= b? (“<=” means less than or equal to)

Answer 5

Evaluate f(a), f(b), and f(c) where c is the x-co-ordinate of the stationary point occuring in the closed interval. This will allow you to say which is the greatest and which is the least value of the function on a <= x <= b.

You need to follow the process for determining the x-co-ordinate of a stationary point.