What is the tangent of f(x)=(x^2)/(x+4),\at x=3 ?

The tangent of f(x)=(x^2)/(x+4),\at x=3 is y= 33/49 x-36/49

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tangent of f(x)=(x^2)/(x+4),\at x=3

tangent of

f (x) = \frac{x ^{2}}{x + 4}, at x = 3

y = \frac{33}{49} x - \frac{36}{49}

Solution steps

Find the tangent point:

(3, \frac{9}{7})

Find the slope of

f (x) = \frac{x ^{2}}{x + 4} : \frac{df ( x )}{d x} = \frac{x ^{2} + 8 x}{( x + 4 ) ^{2}}

Compute the slope of

f (x) = \frac{x ^{2}}{x + 4}

x = 3 : m = \frac{33}{49}

Find the line with slope m=

\frac{33}{49}

and passing through

(3, \frac{9}{7}) : y = \frac{33}{49} x - \frac{36}{49}

y = \frac{33}{49} x - \frac{36}{49}

\frac{d}{d x} (e^{5 x^{4}})

\frac{d y}{d x} + \frac{y}{x} = 9 x + 10

x \to 4 lim (2 x - 5)

\int \frac{4}{x - 3} d x

\frac{d}{d x} (x sin (x) + x cos (x))

What is the tangent of f(x)=(x^2)/(x+4),\at x=3 ?
The tangent of f(x)=(x^2)/(x+4),\at x=3 is y= 33/49 x-36/49