Differentiation

Question 1

What does it mean for a function f to be increasing?

Answer 1

f’(x) is always greater than 0

Question 2

What does it mean for a function f to be decreasing?

Answer 2

f’(x) is always less than 0

Question 3

What is a maximum point of a function?

Answer 3

A point where it stops increasing and begins to decrease

Question 4

What is a minimum point of a function?

Answer 4

A point where it stops decreasing and begins to increase

Question 5

What is a point of inflection of a function?

Answer 5

A point where it changes from being concave to convex, or vice versa

Question 6

What is a stationary point?

Answer 6

A point where f’(x)=0

Question 7

How can the nature of a stationary point be determined using the higher order derivative test?

Answer 7

Find the lowest value of n such that f⁽ⁿ⁺¹⁾(x)≠0. If n is odd and f⁽ⁿ⁺¹⁾(x)<0, it is a maximum point. If n is odd and f⁽ⁿ⁺¹⁾(x)>0, it is a minimum point. If n is even, it is a point of inflection