Question

The approximate value of the function f(x) = x³ − 3x + 5 at x = 1.99 is ____________.

Options

• 7.91

• 7.94

• 6.94

• 6.91

Answer 1

The approximate value of the function f(x) = x³ − 3x + 5 at x = 1.99 is 6.91.

Explanation:

We have, f(x) = x³ − 3x + 5

f'(x) = 3x² − 3

We know that,

∴ f(x + Δx) = f(x) + Δxf'(x)

Here, x + Δx = 1.99

∴ x = 2, Δx = −0.01

∴ f(1.99) = f(2) − 0.01 f'(2)

f(1.99) = (2)³ − 3(2) + 5 − (0.01) (3(2)² − 3)

= (8 − 6 + 5) − (0.01) (9)

= 7 − 0.09

= 6.91