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

The tangent of f(x)= 2/(3x+5),\at a=-1 is y=-6/((3a+5)^2)x+(12a+10)/((3a+5)^2)

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tangent of f(x)= 2/(3x+5),\at a=-1

tangent of

f (x) = \frac{2}{3 x + 5}, at a = - 1

y = - \frac{6}{( 3 a + 5 ) ^{2}} x + \frac{12 a + 10}{( 3 a + 5 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, \frac{2}{3 a + 5})

Find the slope of

f (x) = \frac{2}{3 x + 5} : \frac{df ( x )}{d x} = - \frac{6}{( 3 x + 5 ) ^{2}}

Compute the slope of

f (x) = \frac{2}{3 x + 5}

x = a : m = - \frac{6}{( 3 a + 5 ) ^{2}}

Find the line with slope m=

- \frac{6}{( 3 a + 5 ) ^{2}}

and passing through

(a, \frac{2}{3 a + 5}) : y = - \frac{6}{( 3 a + 5 ) ^{2}} x + \frac{12 a + 10}{( 3 a + 5 ) ^{2}}

y = - \frac{6}{( 3 a + 5 ) ^{2}} x + \frac{12 a + 10}{( 3 a + 5 ) ^{2}}

\int_{0}^{4} π (4 x - x^{2}) d x

x sin (- 2 x) π

9 y^{^{''}} - 7 y = 0

\frac{d}{d x} (\frac{40}{x + 1})

What is the tangent of f(x)= 2/(3x+5),\at a=-1 ?
The tangent of f(x)= 2/(3x+5),\at a=-1 is y=-6/((3a+5)^2)x+(12a+10)/((3a+5)^2)