What is the tangent of f(x)=(x^2)/(x+8),\at x=2 ?

The tangent of f(x)=(x^2)/(x+8),\at x=2 is y= 9/25 x-8/25

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tangent of f(x)=(x^2)/(x+8),\at x=2

tangent of

f (x) = \frac{x ^{2}}{x + 8}, at x = 2

y = \frac{9}{25} x - \frac{8}{25}

Solution steps

Find the tangent point:

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

Find the slope of

f (x) = \frac{x ^{2}}{x + 8} : \frac{df ( x )}{d x} = \frac{x ^{2} + 16 x}{( x + 8 ) ^{2}}

Compute the slope of

f (x) = \frac{x ^{2}}{x + 8}

x = 2 : m = \frac{9}{25}

Find the line with slope m=

\frac{9}{25}

and passing through

(2, \frac{2}{5}) : y = \frac{9}{25} x - \frac{8}{25}

y = \frac{9}{25} x - \frac{8}{25}

\int 10 x ln (9 x) d x

\int_{- π}^{0} sin (x) d x

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

x \to 0 lim (\frac{x ^{2} - 4 x}{x})

x \to 7 + lim (\frac{x - 7}{∣ x - 7 ∣})

What is the tangent of f(x)=(x^2)/(x+8),\at x=2 ?
The tangent of f(x)=(x^2)/(x+8),\at x=2 is y= 9/25 x-8/25