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Use linear approximation, i.e. the tangent line, to approximate 10.1 2 10.12 as follows: Let f ( x ) = x 2 f(x)=x2 and find the equation of the tangent line to f ( x ) f(x) at x = 10 x=10.

User Mindaugasw
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1 Answer

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The linear approximation of a function
f(x) centered at
x=a is


L(x)=f(a)+f'(a)(x-a)

We have


f(x)=x^2\implies f'(x)=2x

and we want to find
L(10.1) for
a=10.

Since
f(10)=100 and
f'(10)=20, we get


10.1^2\approx L(10.1)=100+20(10.1-10)=102

Compare this to the actual value of
10.1^2=102.01.

User Cmorrissey
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