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# Slope Tangent Line to the curve

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Find the slope tangent line to the curve of  $$f(x) =( \sqrt{}x+2) -1$$ at X=2.  Find the equation of tangent line to the function f at x=2 and graph both the function and the tangent line.

$$m= lim_{x\rightarrow 2} = f(x)-f(2) / x-2$$

$$\sqrt{}x+2 -1 - (\sqrt{}x+2 -1) / x-2$$

I believe that the slope will be 1/4 however I'm not sure exactly how to get the answer.

Feb 11, 2019

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f(x) = sqrt(x+2) -1

f'    = 1/ (2(sqrtx+2))      at x = 2   this will give you the slope AT x=2    1 /(2(sqrt2+2)) = 1/4

Feb 11, 2019