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Question
Find a linear approximation for the following functions at the indicated points.
f(x) = x3 – 5x + 12, x0 = 2
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Solution
We know that the linear approximation
L(x) = f(x0) + f’(x0)(x – x0)
f(x) = x3 – 5x + 12
f'(x) = 3x2 – 5
f'(x0) = f'(2) = 12 – 5 = 7
f(x0) = f(2) = 8 – 10 + 12 = 10
L(x) = 10 + 7(x – 2)
= 10 + 7x – 14
= 7x – 4
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