Differentiation

Question 1

How do you find the derivative?

Answer 1

Prepare
Multiply coefficient by power
Take one away from power
Rearrange to remove fractional powers and negative powers

Question 2

What do you do when a fraction, with an x on the bottom, has more than one value on the top. (When wanting to differentiate)

Answer 2

Split the fraction and solve individually

Question 3

How do you simplify a fractional power?

Answer 3

Put x into a square root
Put bottom number in tick
Put top number outside

Question 4

How do you simplify a negative power?

Answer 4

Take it downstairs

Question 5

How do you calculate the rate of change?

Answer 5

Prepare
Differentiate
If x=\_\_\_\_\_
Substitute
Solve

Question 6

What is a tangent?

Answer 6

A straight line at intersects a curve once

Question 7

How do you find the equation of a tangent?

Answer 7

Find y coord by subbing x value into the equation
Find gradient :
- differentiate
- let x=
- subbing in
- solving
Sub into y-b=m(x-a)

Question 8

What pieces of information do you need to calculated the equations of tangents?

Answer 8

Two bits of information

- A point and a gradient

Question 9

What does it mean if dy/dx < 0?

Answer 9

Curve is decreasing

Question 10

What does it mean if dy/dx = 0?

Answer 10

Curve is stationary

Question 11

What does it mean if dy/dx > 0?

Answer 11

Curve is increasing

Question 12

How do you find out whether a curve is increasing, decreasing, or is stationary?

Answer 12

Prepare equation
Differentiate
Let x = \_\_\_\_\_
Substitute
Solve
dy/dx <=> 0
therefore, curve is inc/dec when x = \_\_\_\_\_

Question 13

If a question asks,, Determine whether the curve is increasing, decreasing, or stationary at x = 10,, how do you answer?

Answer 13

Inc and Dec curves
(Prepare
Differentiate
Let x = 10
Solve
dy/dx <=> 0
therefore curve is strictly \_\_\_\_\_\_\_\_)

Question 14

• any number squared is greater than 0*

Question 15

When do stationary points occur?

Answer 15

When dy/dx = 0

Question 16

What are the four types of stationary points?

Answer 16

Max TP
Min TP
Rising Point of Inflection
Falling Point of Inflection

Question 17

How do you find stationary points and work out their nature of the points?

Answer 17

SP's :
- Prepare 
- Differentiate
- 'SP's occur when dy/dx = 0
- Set equation = 0
- Factorise for x values
Partners:
- Sub x values into original equations to find y co ordinates
Table:
- Put x terms into nature table
- State (x,y) is a min/max/rising/falling

Question 18

How do you complete a nature table?

Answer 18

Two columns, three rows
Top row - arrow, x, arrow, x, arrow
Middle row - under x’s = 0, under arrows = sub value into dy/dx, write + or -
Bottom row - draw shape of graph

Question 19

Can be asked to draw graphs

Question 20

If asked to draw a graph, how would you work out the points of interest?

Answer 20

Find TP by differentiating and SP’s =0
‘Cuts x-axis when y=0’ - factorise
‘Cuts y-axis when x=0’

Question 21

What are closed intervals?

Answer 21

The maximum and minimum values present in a section of a graph

Question 22

How do you find the closed intervals?`

Answer 22

Find stationary points
Make sure x values fit in the given range
Substitute all (calculated and given) values into original equation - use table function on calculate
State max and min values 'max value is\_\_\_\_\_\_ when x=\_\_\_\_\_. min value is \_\_\_\_\_\_ when x=\_\_\_\_\_\_'

Question 23

How do you sketch the graphs of derivatives?

Answer 23

Put stationary points on x-axis
Break the curve into sections
If line is going up, put it on top of the x-axis
If line is going down, put it underneath the x-axis

Question 24

What topic is optimisation a part of?

Answer 24

Differentiation

Question 25

How do you do an optimisation question? (part b)

Answer 25

Find stationary points
Sub x into cheating nature table
Decide whether graph is max or min
(Will say in question 'greater amount' = max, 'least amount'=min)
Answer question