What is the tangent of f(x)=(x^2)/(x+9),\at x=1 ?

The tangent of f(x)=(x^2)/(x+9),\at x=1 is y= 19/100 x-9/100

tangent of f(x)=(x^2)/(x+9),\at x=1

tangent of

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

y = \frac{19}{100} x - \frac{9}{100}

Solution steps

Find the tangent point:

(1, \frac{1}{10})

Find the slope of

f (x) = \frac{x ^{2}}{x + 9} : \frac{df ( x )}{d x} = \frac{x ^{2} + 18 x}{( x + 9 ) ^{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{19}{100}

Find the line with slope m=

\frac{19}{100}

and passing through

(1, \frac{1}{10}) : y = \frac{19}{100} x - \frac{9}{100}

y = \frac{19}{100} x - \frac{9}{100}

x \to 0 lim (\frac{x}{x ^{2} + 5 x})

d er i v a t i v e y = x^{4} f (x)

in v erse l a pl a ce \frac{6}{2 s + 1}

\int cot (x) ln (sin (x)) d x

\frac{d}{d x} (\frac{x - 2}{x ^{2} + 5 x + 4})

What is the tangent of f(x)=(x^2)/(x+9),\at x=1 ?
The tangent of f(x)=(x^2)/(x+9),\at x=1 is y= 19/100 x-9/100