MHTCET 2016 Math Solved Paper

(a) Since, f′(x) = x3+5x2 - 7x + 9
After differentiating on both sides w.r.t. x, we get
f ’(x) = 3x2 + 10x - 7
As, f(x +Δx) = f′(x) + Δxf’(x)
= x3+5x2 - 7x + 9 + Δx × (3x2 + 10x - 7)
After putting x = 1 and Δx = 0.1, we get
f(1+o.1) = 13+5(1)2 - 7(1) + 9 + 0.1 x (3 x 12 + 10 x 1 - 7)
So, f(1.1) = 1 + 5 - 7 + 9 + 0.1 (3 + 10 - 7)
= 8 + 0.1 (6) = 8.6