Differentiation

Question 1

How is the instantaneous rate of change defined?

Answer 1

For a function f, it is the limit as h->0 of (f(x+h)-f(x))/h

Question 2

What is a derivative?

Answer 2

An expression that gives the instantaneous rate of change of a function at a given point

Question 3

What two ways can the derivative of a function f be notated?

Answer 3

f’ or dy/dx

Question 4

For a function f(x)=axᵇ where a and b are constants, what is f’(x)?

Answer 4

abxᵇ⁻¹

Question 5

For a function f composed of two other functions g+h, what is f’?

Answer 5

g’+h’

Question 6

What is the second derivative?

Answer 6

The derivative of the derivative

Question 7

What two ways can the second derivative of a function f be notated?

Answer 7

f’’ or (d²y)/(dx²)

Question 8

Given f and f’, how can the instantaneous rate of change at f(a) be calculated?

Answer 8

f’(a)

Question 9

How is the gradient at a point on a curve defined?

Answer 9

As the instantaneous rate of change at that point