Question

Find the approximate value of f(x) = x³ - 3x + 5 at x = 1.99

Answer 1

x = 1.99
now,
1.99^3 = 7.880599 (x^3)
1.99 * 3= 5.97 (3x)
according to the equation,
1.99^3 - 3*1.99 + 5,

7.880599 - 5.97 +5
==>6.910599
hope it helps you if so please mark it as brainliest

Answer 2

Answer :

The approximate value of f(x) = x³ - 3x + 5 at x = 1.99 is 6.91

Step by step explanation :

Hey Mate,

As mention in question we just need to find the approximate value of  f(x) = x³ - 3x + 5 , When X = 1.99

Lets, x = 2 and Δx = - (0.01)

f(x) = x³ - 3x + 5

f'(x) = 3x² - 3

Now,

Δy = f'(x) ×  Δx

Δy = ( 3x² - 3 ) × (- 0.01)

So,

f (x + Δx ) = f(x) + Δy

f (2 + (-0.01)) = ( x³ - 3x + 5 ) +  ( 3x² - 3 ) × (- 0.01)

f (1.99) = ( (2)³ - 3(2) + 5 ) +  ( 3(2)² - 3 ) × (- 0.01)

f (1.99) = ( 8 - 6 + 5 ) +  ( 12 - 3 ) × (- 0.01)

f (1.99) = ( 7 ) +  ( 9 ) × (- 0.01)

f (1.99) = ( 7 ) - ( 0.09 )

f (1.99 ) = 6.91

The approximate value of f(x) = x³ - 3x + 5 at x = 1.99 is 6.91