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

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

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

tangent of

f (x) = 5 x + 6, at a = 2

y = \frac{5}{2 5 a + 6} x + 5 a + 6 - \frac{5 a}{2 5 a + 6}

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, 5 a + 6)

Find the slope of

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

Compute the slope of

f (x) = 5 x + 6

x = a : m = \frac{5}{2 5 a + 6}

Find the line with slope m=

\frac{5}{2 5 a + 6}

and passing through

(a, 5 a + 6) : y = \frac{5}{2 5 a + 6} x + 5 a + 6 - \frac{5 a}{2 5 a + 6}

y = \frac{5}{2 5 a + 6} x + 5 a + 6 - \frac{5 a}{2 5 a + 6}

\frac{d}{d x} (ln (x^{2} - 14 x))

2 x^{2} - 80 x + y^{2} + 49 = 0 (0)

\int_{1}^{2} 4 - x^{2} d x

\int x^{2} \cdot sin (4 x) d x

(x, x^{5}) \to (0, 0) lim (\frac{x ^{5} y}{x ^{10} + y ^{5}})

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