Question

If f(x) = x2 +1, h = 1 then 18 backward difference of Vf(x) Is
given by​

Answer 1

∇f(x) = 2x - 1

Given :

f(x) = x² + 1 , h = 1

To find :

The backward difference ∇f(x)

Solution :

Step 1 of 2 :

Find f(x - h)

Here it is given that

f(x) = x² + 1 , h = 1

Thus we get

f(x - h)

= f(x - 1)

= (x - 1)² + 1

= x² - 2x + 1 + 1

= x² - 2x + 2

Step 2 of 2 :

Find the backward difference ∇f(x)

∇f(x)

= f(x) - f(x - h)

= f(x) - f(x - 1)

= ( x² + 1 ) - ( x² - 2x + 2 )

= x² + 1 - x² + 2x - 2

= 2x - 1

Correct question : If f(x) = x² + 1 , h = 1 then backward difference ∇f(x) is given by

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