What is the tangent of f(x)= x/(x+100),\at x=50 ?

The tangent of f(x)= x/(x+100),\at x=50 is y= 1/225 x+1/9

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tangent of f(x)= x/(x+100),\at x=50

tangent of

f (x) = \frac{x}{x + 100}, at x = 50

y = \frac{1}{225} x + \frac{1}{9}

Solution steps

Find the tangent point:

(50, \frac{1}{3})

Find the slope of

f (x) = \frac{x}{x + 100} : \frac{df ( x )}{d x} = \frac{100}{( x + 100 ) ^{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{1}{225}

Find the line with slope m=

\frac{1}{225}

and passing through

(50, \frac{1}{3}) : y = \frac{1}{225} x + \frac{1}{9}

y = \frac{1}{225} x + \frac{1}{9}

\frac{d}{d x} (\frac{x - 5}{x + 1})

\int tan (x) \cdot sec (x) d x

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

x^{4} - x^{5} y^{2} = - 3, (1, 2)

\frac{d}{d x} (- \frac{21}{x ^{4}})

What is the tangent of f(x)= x/(x+100),\at x=50 ?
The tangent of f(x)= x/(x+100),\at x=50 is y= 1/225 x+1/9