Differentiation

Question 1

How to identify increasing / decreasing

Answer 1

Prove f’x always positive or negative

Question 1

First principles

Answer 1

lim
h -> 0

h

Question 2

What does it mean if f’‘x is 0

Answer 2

Look at gradient either side

Question 3

Sketching diff

Answer 3

If postive or negative gradient:
Above or below X axis

If gradient increasing or decreasing:
Line going up or down

Question 4

Differentiations from first principles trig

Answer 4

Use double angle formulae

Use small angle approx to get:
sin(h)
——- = 1
h

cos(h) - 1
———— = 0
h

Question 5

Calculus with trig:

Answer 5

Angles are in radians

Question 6

Differentiate reciprocal

Answer 6

Use (trig)^-1 and use chain rule

Question 7

Differentiate inverse

Answer 7

trig both sudes to get
x = trig(y)

differentiate

use sin^2 + cos^2 = 1 to convert

Question 8

Convex and concave

Answer 8

Convex increasing GRADIENT
Concave decreasing GRADIENT

Question 9

Find convex / concave

Answer 9

Use double diff, look at sign to see if its more or less than 0

Question 10

Point of inflection

Answer 10

Where f’‘x = 0 AND change of convex / concave

Analyse sign before and after

Question 11

ln(f(x)) diff

Answer 11

f’x/fx