Concept: Let small charge in x be ?x and the corresponding change in y is ?y.\(\rm ? y = \rm \dfrac{dy}{dx}? x = f'(x) ? x \)Now that ?y = f(x + ?x) - f(x)Therefore, f(x + ?x) = f(x) + ?yCalculation: Given: f (x) = 2x2 + x + 2.f'(x) = 4x + 1Let x + ?x = 2.002 = 2 + 0.002Therefore, x = 2 and ?x = 0.002f(x + ?x) = f(x) + ?y= f(x + ?x) = f(x) + f'(x)?x= f(2.002) = 2x2 + x + 2 + (4x + 1)?x= 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