Differentiation 1

Question 1

How do you notate differentiation?

Answer 1

𝑓′(𝑥) and 𝑑𝑦/𝑑𝑥
-both represent the derivative.

You normally use 𝑑𝑦/𝑑𝑥 when you are given an expression in the form 𝑦 = ⋯

You normally use 𝑓′(𝑥) when you are given an expression in the form 𝑓(𝑥) = ⋯

Question 2

How do you differentiate polynomials?

Answer 2

Multiply by the power, then take one from the power.

Question 3

How should you rewrite expressions to differentiate?

Answer 3

To differentiate, you must first rewrite the expression in index form.

When rewriting, only rewrite the
algebraic terms.

Numbers do not change

Question 4

How do you find the gradient of a tangent to a curve?

Answer 4

Find the gradient function, then sub in the x ordinate given.

Question 5

How do you find the gradient of a normal to a curve?

Answer 5

Find the gradient function, then sub in the x ordinate given. (Grad of tangent)

Then the negative reciprocal of this is the gradient of the normal.

Question 6

How do you find stationary points?

Answer 6

When the gradient function is equal to 0, it is at a stationary point.

Set the gradient function equal to 0.
Then solve.

Question 7

How do you find and notate the second derivative?

Answer 7

The second derivative is found when
differentiating the gradient function.

The notation for the second derivative is 𝑑²𝑦/𝑑𝑥² or 𝑓′′(𝑥).

Question 8

How do you determine the nature of a stationary point?

Answer 8

Put the x ordinate of the stationary point into the second derivative, then if:

𝑑²𝑦/𝑑𝑥² > 0, the stationary point is a minimum

𝑑²𝑦/𝑑𝑥² < 0, the stationary point is a maximum

Question 9

What does it mean if E.g. a line and a curve ‘touch’?

Answer 9

It means there is one point of intersection.

Question 10

How do you know if a function is increasing or decreasing?

Answer 10

Increasing function- gradient is positive

Decreasing function- gradient is negative