Differentiation

Question 1

What are the 3 marks of an optimisation question part a awarded for?

Answer 1

2 formulas in 2 variables (1 mark for each) then another mark for blending together into 1 formula, 1 variable which is given in the question.

Question 2

What mnemonic do we use to help us remember the 6 steps of an optimisation part b question? (And what do each of the letter stand for)

Answer 2

Differentiate formula given in part a
Equate the derivative to 0
Solve it
If necessary, sub your answer into part a
formula
Grow a nature table
Nice statement to conclude

Question 3

What is the relationship between Displacement, Velocity and Acceleration?

Answer 3

Dave’s Very Amazing traffic light.

Derivative of D is V, derivative of V is A, double derivative of D is A.

Integral of A is V, integral of V is D, double integral of A is D.

Question 4

What is the second derivative test?
What is it used for and what do the answers mean?

Answer 4

It’s used to find the nature of turning points:

If f’’(x) > 0 then turning point is a minimum.
If f’’(x) < 0 then turning point is a maximum.
If f’’(x) = 0 then inconclusive so nature table required.

Question 5

How do you ‘prepare for calculus’?

i.e. x^3+x/(Square root of x)

Answer 5

Split into individual fractions then combine each fraction into a single x^n term

i.e. x^3+x/(square root of x) = x^3+x/x^1/2
= x^3/x^1/2+x/x^1/2 = x^5/2+x^1/2

Question 6

What is the discriminant and what is it used for?

Answer 6

b^2-4ac

Used to find the nature of roots of a quadratic.

Question 7

How do you differentiate a term?

Answer 7

(1) Multiply by the current power
(2) Decrease the power by one

Question 8

When do we use the chain rule for differentiation? What is the extra 3rd step we need to take over and above normal differentiating?

Answer 8

When differentiating sinx or cosx to a power (i.e. sin^3 x) or when differentiating a bracketed term to a power when the bracket has it’s own derivative i.e. (3x+1)^5
We need to multiply also by the derivative of sin/cos or the brackets.

Question 9

Why do we differentiate?

Answer 9

•Question says so
•To find range of change
•To find the gradient of a tangent to a curve
•To find velocity from displacement or acceleration from velocity