Question

EXERCISE 14 (d) Find the derivative of the following func tions 'ab initio', that is, using the definition (I) 2x³ (ii) x⁴ (iii) x²+1
​

Answer 1

Answer:

Let f(x)=x

3

−27

According to the first principle,

(x)=

h→0

lim

h

f(x+h)−f(x)

=

h→0

lim

h

[(x+h)

3

−27]−(x

3

−27)

=

h→0

lim

h

x

3

+h

3

+3x

2

h+3xh

2

−x

3

=

h→0

lim

h

h

3

+3x

2

h+3xh

2=

h→0

lim

(h

2

+3x

2

+3xh)

= 0+3x

2

+0=3x

2