What is the tangent of f(x)= 5/(2sqrt(5x+6)),\at x=6 ?

The tangent of f(x)= 5/(2sqrt(5x+6)),\at x=6 is y=-25/864 x+85/144

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tangent of f(x)= 5/(2sqrt(5x+6)),\at x=6

tangent of

f (x) = \frac{5}{2 5 x + 6}, at x = 6

y = - \frac{25}{864} x + \frac{85}{144}

Solution steps

Find the tangent point:

(6, \frac{5}{12})

Find the slope of

f (x) = \frac{5}{2 5 x + 6} : \frac{df ( x )}{d x} = - \frac{25}{4 ( 5 x + 6 ) ^{\frac{3}{2}}}

Compute the slope of

f (x) = \frac{5}{2 5 x + 6}

x = 6 : m = - \frac{25}{864}

Find the line with slope m=

- \frac{25}{864}

and passing through

(6, \frac{5}{12}) : y = - \frac{25}{864} x + \frac{85}{144}

y = - \frac{25}{864} x + \frac{85}{144}

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What is the tangent of f(x)= 5/(2sqrt(5x+6)),\at x=6 ?
The tangent of f(x)= 5/(2sqrt(5x+6)),\at x=6 is y=-25/864 x+85/144