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

The tangent of f(x)= 5/(2sqrt(5x+6)),\at a=2 is y=-(25)/(4(5a+6)^{3/2)}x+(75a+60)/(4(5a+6)^{3/2)}

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

tangent of

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

y = - \frac{25}{4 ( 5 a + 6 ) ^{\frac{3}{2}}} x + \frac{75 a + 60}{4 ( 5 a + 6 ) ^{\frac{3}{2}}}

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, \frac{5}{2 5 a + 6})

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}{4 ( 5 a + 6 ) ^{\frac{3}{2}}}

Find the line with slope m=

- \frac{25}{4 ( 5 a + 6 ) ^{\frac{3}{2}}}

and passing through

(a, \frac{5}{2 5 a + 6}) : y = - \frac{25}{4 ( 5 a + 6 ) ^{\frac{3}{2}}} x + \frac{75 a + 60}{4 ( 5 a + 6 ) ^{\frac{3}{2}}}

y = - \frac{25}{4 ( 5 a + 6 ) ^{\frac{3}{2}}} x + \frac{75 a + 60}{4 ( 5 a + 6 ) ^{\frac{3}{2}}}

What is the tangent of f(x)= 5/(2sqrt(5x+6)),\at a=2 ?
The tangent of f(x)= 5/(2sqrt(5x+6)),\at a=2 is y=-(25)/(4(5a+6)^{3/2)}x+(75a+60)/(4(5a+6)^{3/2)}