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

The tangent of f(x)= 5/(2sqrt(5x+6)),\at x=2 is y=-25/256 x+105/128

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

tangent of

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

y = - \frac{25}{256} x + \frac{105}{128}

Solution steps

Find the tangent point:

(2, \frac{5}{8})

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}}}

EN : T i tl e G e n er a l Eq u a t i o n Sl o p e A t P o in t 2 Eq : m = - \frac{25}{256}

Find the line with slope m=

- \frac{25}{256}

and passing through

(2, \frac{5}{8}) : y = - \frac{25}{256} x + \frac{105}{128}

y = - \frac{25}{256} x + \frac{105}{128}

What is the tangent of f(x)= 5/(2sqrt(5x+6)),\at x=2 ?
The tangent of f(x)= 5/(2sqrt(5x+6)),\at x=2 is y=-25/256 x+105/128