What is the tangent of f(x)=(11)/(9x),\at x=1 ?

The tangent of f(x)=(11)/(9x),\at x=1 is y=-11/9 x+22/9

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tangent of f(x)=(11)/(9x),\at x=1

tangent of

f (x) = \frac{11}{9 x}, at x = 1

y = - \frac{11}{9} x + \frac{22}{9}

Solution steps

Find the tangent point:

(1, \frac{11}{9})

Find the slope of

f (x) = \frac{11}{9 x} : \frac{df ( x )}{d x} = - \frac{11}{9 x ^{2}}

Compute the slope of

f (x) = \frac{11}{9 x}

x = 1 : m = - \frac{11}{9}

Find the line with slope m=

- \frac{11}{9}

and passing through

(1, \frac{11}{9}) : y = - \frac{11}{9} x + \frac{22}{9}

y = - \frac{11}{9} x + \frac{22}{9}

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

f (x) = \frac{10}{x ^{2}}

\int \frac{1}{x 4 ^{2} - 9} d x

\int \frac{1}{1 - \frac{1}{2} x} d x

\frac{x}{6}

What is the tangent of f(x)=(11)/(9x),\at x=1 ?
The tangent of f(x)=(11)/(9x),\at x=1 is y=-11/9 x+22/9