What is the tangent of f(x)=x^{1/2},(81,9) ?

The tangent of f(x)=x^{1/2},(81,9) is y= 1/18 x+9/2

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tangent of f(x)=x^{1/2},(81,9)

tangent of

f (x) = x^{\frac{1}{2}}, (81, 9)

y = \frac{1}{18} x + \frac{9}{2}

Solution steps

Find the slope of

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

Compute the slope of

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

(81, 9) : m = \frac{1}{18}

Find the line with slope m=

\frac{1}{18}

and passing through

(81, 9) : y = \frac{1}{18} x + \frac{9}{2}

y = \frac{1}{18} x + \frac{9}{2}

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What is the tangent of f(x)=x^{1/2},(81,9) ?
The tangent of f(x)=x^{1/2},(81,9) is y= 1/18 x+9/2