What is the tangent of f(x)= 2/(x+7) ?

The tangent of f(x)= 2/(x+7) is y=-2/((a_{0)+7)^2}x+(4a_{0}+14)/((a_{0)+7)^2}

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tangent of f(x)= 2/(x+7)

tangent of

f (x) = \frac{2}{x + 7}

y = - \frac{2}{( a _{0} + 7 ) ^{2}} x + \frac{4 a _{0} + 14}{( a _{0} + 7 ) ^{2}}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, \frac{2}{a _{0} + 7})

Find the slope of

f (x) = \frac{2}{x + 7} : \frac{df ( x )}{d x} = - \frac{2}{( x + 7 ) ^{2}}

Compute the slope of

f (x) = \frac{2}{x + 7}

x = a_{0} : m = - \frac{2}{( a _{0} + 7 ) ^{2}}

Find the line with slope m=

- \frac{2}{( a _{0} + 7 ) ^{2}}

and passing through

(a_{0}, \frac{2}{a _{0} + 7}) : y = - \frac{2}{( a _{0} + 7 ) ^{2}} x + \frac{4 a _{0} + 14}{( a _{0} + 7 ) ^{2}}

y = - \frac{2}{( a _{0} + 7 ) ^{2}} x + \frac{4 a _{0} + 14}{( a _{0} + 7 ) ^{2}}

\int x cos (3) x^{2} d x

\frac{d}{d x} (5 x^{4} + 3 x^{2} - 9 x + 16)

f (x) = 7 e^{x} + x, (0, 7)

\int \frac{2 - v}{v ^{2} - 1} d v

f (x) = x - 2, g (x) = - x^{2} + x + 2

What is the tangent of f(x)= 2/(x+7) ?
The tangent of f(x)= 2/(x+7) is y=-2/((a_{0)+7)^2}x+(4a_{0}+14)/((a_{0)+7)^2}