What is the tangent of f(x)=sqrt(x),\at x=5 ?

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

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tangent of f(x)=sqrt(x),\at x=5

tangent of

f (x) = x, at x = 5

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

Solution steps

Find the tangent point:

(5, 5)

Find the slope of

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

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}{2 5}

Find the line with slope m=

\frac{1}{2 5}

and passing through

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

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

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