What is the tangent of f(x)= 5/(2sqrt(5x+4)),\at x=9 ?

The tangent of f(x)= 5/(2sqrt(5x+4)),\at x=9 is y=-25/1372 x+715/1372

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tangent of f(x)= 5/(2sqrt(5x+4)),\at x=9

tangent of

f (x) = \frac{5}{2 5 x + 4}, at x = 9

y = - \frac{25}{1372} x + \frac{715}{1372}

Solution steps

Find the tangent point:

(9, \frac{5}{14})

Find the slope of

f (x) = \frac{5}{2 5 x + 4} : \frac{df ( x )}{d x} = - \frac{25}{4 ( 5 x + 4 ) ^{\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}{1372}

Find the line with slope m=

- \frac{25}{1372}

and passing through

(9, \frac{5}{14}) : y = - \frac{25}{1372} x + \frac{715}{1372}

y = - \frac{25}{1372} x + \frac{715}{1372}

What is the tangent of f(x)= 5/(2sqrt(5x+4)),\at x=9 ?
The tangent of f(x)= 5/(2sqrt(5x+4)),\at x=9 is y=-25/1372 x+715/1372