Differentiation

Question 1

What are the basic rules of differentiation

Answer 1

Multiply by power and decrease by one

Question 2

To differentiate all variables have to be

Answer 2

• on the numerator
• written in index form

Question 3

What to do if there are dividing indices

Answer 3

Subtract them

Question 4

What does positive rate of change indicate

Answer 4

Increasing

Question 5

What does negative rate of change indicate

Answer 5

Decreasing

Question 6

What two things do we need to find equation of tangent

Answer 6

• coordinates of the point where it meets the curve
• the gradient at that point

Question 7

If you’re given the gradient and an equation what to

Answer 7

The derivative of the equation is equals to the gradient and factorise to find x

Question 8

To prove a curve is never decreasing

Answer 8

Differentiation and factorise need square

Question 9

When do stationary points occur

Answer 9

Stationary points occur when f’(x) =0

Question 10

What is the nature of sp when increasing from left to right

Answer 10

Rising point of inflection

Question 11

What is the nature of sp when decreasing from left to right

Answer 11

Falling point of inflection

Question 12

What is the method of finding stationary points and their nature

Answer 12

• differentiate the function
• find the stationary values by solving f’(x)=0
• find the stationary points (y coordinate by subbing into original eqn)
• determine nature by subbing appropriate values into derivative

Question 13

In order to sketch the graph of a function we need

Answer 13

• the roots (or x-intercepts) - cuts x axis when y=0
• the y intercept- cuts y-axis when x=0
• stationary points and their nature
• the behaviour of the curve for large positive and negative values of x

Question 14

Closed intervals (find the minimum and maximum value of derivative?)

Answer 14

• calculate the y values at each end of the given range
• differentiate and set to zero to find the x values of sp
• find y coordinate of sp
• compare the y coordinates and make a statement regarding max and minimum

Question 15

How to sketch the graph of a derived function

Answer 15

• identify the gradient along the curve (positive negative zero)
• make the stationary points the roots
• shade in weather the gradient is positive or negative to each side of the sp
• sketch a graph through shaded areas

Question 16

To do part b of optimisation

Answer 16

1- differentiate
2- sp occur when f’(x)=0
3- solve for x
4- nature table to prove it is a maximum or minimum
5- answer question does it ask for the value of x, the area, the volume?