Discussion Forum

 Using differentiation , approximate value of  f(x)= x²-2x+1  at x=2.99 is

Answer:

Explanation:

Given function ,   f(x)= x²-2x+1 

 $\Rightarrow$  f'(x)=  2x-2

 Let x=3 and $\triangle$ x=-0.01

 so that f(x+$\triangle$ x)= f(2.99)

 We know that , f(x+$\triangle$ x)≈ f(x)+ $\triangle$ x f'(x)

≈ (x²-2x+1)+(-0.01)(2x-2)

 putting x=3 and $\triangle$ x= -0.01, we get

 f(2.99) ≈  (3²-2 x3+1)-(-0.01)(2 x3-2)

≈(4) +(-0.01)(4)

≈  4-0.04≈ 3.96