What is the tangent of (2x-1)/(x+3),\at x=4 ?

The tangent of (2x-1)/(x+3),\at x=4 is y= 1/7 x+3/7

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tangent of (2x-1)/(x+3),\at x=4

tangent of

\frac{2 x - 1}{x + 3}, at x = 4

y = \frac{1}{7} x + \frac{3}{7}

Solution steps

Find the tangent point:

(4, 1)

Find the slope of

y = \frac{2 x - 1}{x + 3} : \frac{d y}{d x} = \frac{7}{( x + 3 ) ^{2}}

Compute the slope of

y = \frac{2 x - 1}{x + 3}

x = 4 : m = \frac{1}{7}

Find the line with slope m=

\frac{1}{7}

and passing through

(4, 1) : y = \frac{1}{7} x + \frac{3}{7}

y = \frac{1}{7} x + \frac{3}{7}

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What is the tangent of (2x-1)/(x+3),\at x=4 ?
The tangent of (2x-1)/(x+3),\at x=4 is y= 1/7 x+3/7