13) Differentiation

Question 1

Explain how to draw a derivative graph for a curve ?

Answer 1

• When the gradient is increasing, the derivative graph will be positive ( positive y value )
• When the gradient is decreasing, the derivative graph will be negative ( negative y value )
• When the graph has a stationary point, the derivative graph will cross the x axis

Question 2

What does the first derivative show ?

Answer 2

• The gradient of a graph at a specific point
• Whether a function is increasing or decreasing

Question 3

What does the second derivative show ?

Answer 3

• Whether a stationary point is a minimum or a maximum
• Whether the gradient is increasing or decreasing

Question 4

When does the first derivative show whether a function is increasing or decreasing ?

Answer 4

• dy/dx > 0 , this means the function is increasing
• dy/dx < 0 , this means the function is decreasing

Question 5

What do you use to find the ‘rate of change’ ?

Answer 5

The first derivative

Question 6

What do you use to find the ‘rate of the rate of change’ ?

Answer 6

The second derivative

Question 7

When does the second derivative sow that the gradient is increasing or decreasing ?

Answer 7

• d^2y/dx^2 > 0 the gradient is increasing
• d^2y/dx^2 < 0 the gradient is decreasing

Question 8

When does the second derivative show whether a stationary point is a local maximum or local minimum ?

Answer 8

• d^2y/dx^2 > 0 the point is a local minimum
• d^2y/dx^2 < 0 the point is a local maximum

Question 9

How else can dy/dx be phrased ?

Answer 9

• The rate of change of y with respect to x
• How fast y changes when x is changed