What is the tangent of f(x)=((x^2))/(x+9),\at x=2 ?

The tangent of f(x)=((x^2))/(x+9),\at x=2 is y= 40/121 x-36/121

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tangent of f(x)=((x^2))/(x+9),\at x=2

tangent of

f (x) = \frac{( x ^{2} )}{x + 9}, at x = 2

y = \frac{40}{121} x - \frac{36}{121}

Solution steps

Find the tangent point:

(2, \frac{4}{11})

Find the slope of

f (x) = \frac{x ^{2}}{x + 9} : \frac{df ( x )}{d x} = \frac{x ^{2} + 18 x}{( x + 9 ) ^{2}}

Compute the slope of

f (x) = \frac{x ^{2}}{x + 9}

x = 2 : m = \frac{40}{121}

Find the line with slope m=

\frac{40}{121}

and passing through

(2, \frac{4}{11}) : y = \frac{40}{121} x - \frac{36}{121}

y = \frac{40}{121} x - \frac{36}{121}

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\int \frac{1}{( x + 1 ) ^{2} ( x - 3 )} d x

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\int_{0}^{1} (u + 7) (u - 8) d u

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What is the tangent of f(x)=((x^2))/(x+9),\at x=2 ?
The tangent of f(x)=((x^2))/(x+9),\at x=2 is y= 40/121 x-36/121