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

The tangent of f(x)=(x+3)/(2x+1),\at x=-1 is y=-5x-7

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

tangent of

f (x) = \frac{x + 3}{2 x + 1}, at x = - 1

y = - 5 x - 7

Solution steps

Find the tangent point:

(- 1, - 2)

Find the slope of

f (x) = \frac{x + 3}{2 x + 1} : \frac{df ( x )}{d x} = - \frac{5}{( 2 x + 1 ) ^{2}}

Compute the slope of

f (x) = \frac{x + 3}{2 x + 1}

x = - 1 : m = - 5

Find the line with slope m=

- 5

and passing through

(- 1, - 2) : y = - 5 x - 7

y = - 5 x - 7

2 x^{- \frac{1}{4}}

x \to \infty lim (9^{x})

\frac{d}{d x} (\frac{1}{1 + ln ( x )})

y^{^{'}} - \frac{y}{x} = \frac{x y}{x}

\frac{d x}{d t} = x + \frac{t ^{2}}{2}, x (0) = 0

What is the tangent of f(x)=(x+3)/(2x+1),\at x=-1 ?
The tangent of f(x)=(x+3)/(2x+1),\at x=-1 is y=-5x-7