What is the tangent of f(x)=(2x+1)^{1/2},\at x=2 ?

The tangent of f(x)=(2x+1)^{1/2},\at x=2 is y= 1/(5^{1/2)}x+5^{1/2}-2/(5^{1/2)}

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tangent of f(x)=(2x+1)^{1/2},\at x=2

tangent of

f (x) = (2 x + 1)^{\frac{1}{2}}, at x = 2

y = \frac{1}{5 ^{\frac{1}{2}}} x + 5^{\frac{1}{2}} - \frac{2}{5 ^{\frac{1}{2}}}

Solution steps

Find the tangent point:

(2, 5^{\frac{1}{2}})

Find the slope of

f (x) = (2 x + 1)^{\frac{1}{2}} : \frac{df ( x )}{d x} = \frac{1}{( 2 x + 1 ) ^{\frac{1}{2}}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = \frac{1}{5 ^{\frac{1}{2}}}

Find the line with slope m=

\frac{1}{5 ^{\frac{1}{2}}}

and passing through

(2, 5^{\frac{1}{2}}) : y = \frac{1}{5 ^{\frac{1}{2}}} x + 5^{\frac{1}{2}} - \frac{2}{5 ^{\frac{1}{2}}}

y = \frac{1}{5 ^{\frac{1}{2}}} x + 5^{\frac{1}{2}} - \frac{2}{5 ^{\frac{1}{2}}}

What is the tangent of f(x)=(2x+1)^{1/2},\at x=2 ?
The tangent of f(x)=(2x+1)^{1/2},\at x=2 is y= 1/(5^{1/2)}x+5^{1/2}-2/(5^{1/2)}