linearization

spezialize

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Sep 27, 2005
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I need to find the linearization for L(x) for f(x)= sqrt(x+1) at x=3.. can anyone give me some steps on how to go about for solving this.
 
Well L(x)=f(a)+f(a)(xa)\displaystyle L(x) = f(a) + f'(a)(x - a) here a=3.

Also f(x)=x+1,f(x)=12x+1\displaystyle f(x) = \sqrt {x + 1} ,\quad f'(x) = \frac{1}{{2\sqrt {x + 1} }}
 
f(3)=3+1=2\displaystyle f(3) = \sqrt {3 + 1} = 2

f(3)=123+1=14\displaystyle f'(3) = \frac{1}{{2\sqrt {3 + 1} }} = \frac{1}{4}

L(x)=2+14(x3)\displaystyle L(x) = 2 + \frac{1}{4}(x - 3)
 
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