Question

The approximate value of f(x) = x³ + 5x² – 7x + 9 at x = 1.1 is ______.

Options

• 8.6

• 8.5

• 8.4

• 8.3

Answer 1

The approximate value of f(x) = x³ + 5x² – 7x + 9 at x = 1.1 is 8.6.

Explanation:

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 + 0.1) = 1³ + 5(1)² – 7(1) + 9 + 0.1 × (3 × 1² + 10 × 1 – 7)

So, f(1.1) = 1 + 5 – 7 + 9 + 0.1 (3 + 10 – 7)

= 8 + 0.1(6)

= 8.6