What is the tangent of f(x)=(9x)/(x+4),\at x=8 ?

The tangent of f(x)=(9x)/(x+4),\at x=8 is y= 1/4 x+4

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tangent of f(x)=(9x)/(x+4),\at x=8

tangent of

f (x) = \frac{9 x}{x + 4}, at x = 8

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

Solution steps

Find the tangent point:

(8, 6)

Find the slope of

f (x) = \frac{9 x}{x + 4} : \frac{df ( x )}{d x} = \frac{36}{( x + 4 ) ^{2}}

Compute the slope of

f (x) = \frac{9 x}{x + 4}

x = 8 : m = \frac{1}{4}

Find the line with slope m=

\frac{1}{4}

and passing through

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

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

\int - \frac{1}{4} sin (2 x) d x

f (x) = \frac{6 x}{x + 6}

\frac{d}{d x} (ln (3 x^{2} + 5))

36 y^{^{''}} - 12 y^{^{'}} + y = 0

x \to 0 + lim (x^{2} - ln (x))

What is the tangent of f(x)=(9x)/(x+4),\at x=8 ?
The tangent of f(x)=(9x)/(x+4),\at x=8 is y= 1/4 x+4