What is the tangent of f(x)= 8/(sqrt(x+11)),\at x=5 ?

The tangent of f(x)= 8/(sqrt(x+11)),\at x=5 is y=-1/16 x+37/16

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tangent of f(x)= 8/(sqrt(x+11)),\at x=5

tangent of

f (x) = \frac{8}{x + 11}, at x = 5

y = - \frac{1}{16} x + \frac{37}{16}

Solution steps

Find the tangent point:

(5, 2)

Find the slope of

f (x) = \frac{8}{x + 11} : \frac{df ( x )}{d x} = - \frac{4}{( x + 11 ) ^{\frac{3}{2}}}

Compute the slope of

f (x) = \frac{8}{x + 11}

x = 5 : m = - \frac{1}{16}

Find the line with slope m=

- \frac{1}{16}

and passing through

(5, 2) : y = - \frac{1}{16} x + \frac{37}{16}

y = - \frac{1}{16} x + \frac{37}{16}

\int_{0}^{1} 3 x d x

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

(x - 1)^{2}, x + 1

y = (t + 3) in (t)

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

What is the tangent of f(x)= 8/(sqrt(x+11)),\at x=5 ?
The tangent of f(x)= 8/(sqrt(x+11)),\at x=5 is y=-1/16 x+37/16