What is the tangent of f(x)=(4x)/(x+3),(1,1) ?

The tangent of f(x)=(4x)/(x+3),(1,1) is y= 3/4 x+1/4

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tangent of f(x)=(4x)/(x+3),(1,1)

tangent of

f (x) = \frac{4 x}{x + 3}, (1, 1)

y = \frac{3}{4} x + \frac{1}{4}

Solution steps

Find the slope of

f (x) = \frac{4 x}{x + 3} : \frac{df ( x )}{d x} = \frac{12}{( x + 3 ) ^{2}}

Compute the slope of

f (x) = \frac{4 x}{x + 3}

(1, 1) : m = \frac{3}{4}

Find the line with slope m=

\frac{3}{4}

and passing through

(1, 1) : y = \frac{3}{4} x + \frac{1}{4}

y = \frac{3}{4} x + \frac{1}{4}

\frac{d}{d θ} (cos (θ) - θ sin (θ))

9 x^{2}, 8 x^{4} - 8 x^{2}

\frac{d y}{d x} + 2 x^{2} = 0

\int \frac{e ^{x}}{e ^{x} + 6} d x

x e^{- \frac{1}{x}}

What is the tangent of f(x)=(4x)/(x+3),(1,1) ?
The tangent of f(x)=(4x)/(x+3),(1,1) is y= 3/4 x+1/4