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

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

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

tangent of

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

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

Solution steps

Find the tangent point:

(3, 3)

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}

x = 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}

x \to - 4 lim (\frac{∣ x + 4 ∣}{x + 4})

y = (e^{4 x} - 3)^{8}

\frac{d ^{3}}{d x ^{3}} (2 x^{3} - 4 x^{2} + 2)

x^{3} - 5 x, 4 x

\frac{d}{d x} (\frac{7}{x + 4})

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