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Question
Find the approximate values of : f(x) = x3 + 5x2 – 7x + 10 at x = 1.12.
Solution
f(x) = x3 + 5x2 – 7x + 10
∴ f'(x) = `d/dx(x^3 + 5x^2 - 7x + 10)`
= 3x2 + 5 x 2x – 7 x 1 + 0
= 3x2 + 10x – 7
Take a = 1, h = 0.12
Then f(a) = f(1)
= (1)3 + 5(1)2 – 7(1) + 10
= 1 + 5 – 7 + 10
= 9
and
f'(a) = f'(1)
= 3(1)2 + 10(1) – 7
= 3 + 10 – 7
= 6
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ f(1.12) = f(1 + 0.12)
≑ f(1) + (0.12).f'(1)
≑ 9 + 0.12 x 6
≑ 9 + 0.72
= 9.72
∴ f(1.12) ≑ 9.72.
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