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

The tangent of f(x)=(4x)/(x+1),(3,3) is y= 1/4 x+9/4

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

tangent of

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

y = \frac{1}{4} x + \frac{9}{4}

Solution steps

Find the slope of

f (x) = \frac{4 x}{x + 1} : \frac{df ( x )}{d x} = \frac{4}{( x + 1 ) ^{2}}

Compute the slope of

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

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

Find the line with slope m=

\frac{1}{4}

and passing through

(3, 3) : y = \frac{1}{4} x + \frac{9}{4}

y = \frac{1}{4} x + \frac{9}{4}

f (x) = 3 x + 1

\frac{d}{d x} ((ln (x))^{s i n (x)})

\frac{d y}{d t} = \frac{y}{t + 1} + 4 t^{2} + 4 t, y (1) = 6

\frac{d}{d x} ((A x + B) e^{2 x})

x \to 3 lim (5 x^{2} - 7 x - 3)

What is the tangent of f(x)=(4x)/(x+1),(3,3) ?
The tangent of f(x)=(4x)/(x+1),(3,3) is y= 1/4 x+9/4