Differentiationof Polynomials

f(x) = axn

then f’x) = anxn-1

Derivative = gradient = rate of change

Graphsf’(x)=0

54

2( )

3f x

x

5

42( )

3

xf x

9

4

94

552'( )

3 6

xf x

x

1

2( ) 2 1f x x x 3 1

2 2( ) 2f x x x 1 1

2 21

'( ) 32

f x x x

1

21

'( ) 32

f x xx

f’(x)=0Stationary PtsMax. / Mini Pts

Inflection Pt

Nature Table

Max

-1 2 5+ 0 -

xf’(x)

Gradient at a point

Equation of tangent line

Straight LineTheory

Leibniz Notation

'( )dy

f xdx