Correct Answer - Option 3 : 12.018
Concept:
Let small charge in x be Δx and the corresponding change in y is Δy.
\(\rm Δ y = \rm \dfrac{dy}{dx}Δ x = f'(x) Δ x \)
Now that Δy = f(x + Δx) - f(x)
Therefore, f(x + Δx) = f(x) + Δy
Calculation:
Given: f (x) = 2x2 + x + 2.
f'(x) = 4x + 1
Let x + Δx = 2.002 = 2 + 0.002
Therefore, x = 2 and Δx = 0.002
f(x + Δx) = f(x) + Δy
= f(x + Δx) = f(x) + f'(x)Δx
= f(2.002) = 2x2 + x + 2 + (4x + 1)Δx
= f(2.002) = 2(2)2 + 2 + 2 + [4⋅(2) + 1](0.002)
= f(2.002) = 12 + (9)(0.002)
= f(2.002) = 12 + 0.018
= f(2.002) = 12.018
