What is the tangent of f(x)=sqrt(3x+7),\at a=6 ?

The tangent of f(x)=sqrt(3x+7),\at a=6 is y= 3/(2sqrt(3a+7))x+sqrt(3a+7)-(3a)/(2sqrt(3a+7))

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tangent of f(x)=sqrt(3x+7),\at a=6

tangent of

f (x) = 3 x + 7, at a = 6

y = \frac{3}{2 3 a + 7} x + 3 a + 7 - \frac{3 a}{2 3 a + 7}

Solution steps

Compute the tangent line to the general point

x = a

Find the tangent point:

(a, 3 a + 7)

Find the slope of

f (x) = 3 x + 7 : \frac{df ( x )}{d x} = \frac{3}{2 3 x + 7}

Compute the slope of

f (x) = 3 x + 7

x = a : m = \frac{3}{2 3 a + 7}

Find the line with slope m=

\frac{3}{2 3 a + 7}

and passing through

(a, 3 a + 7) : y = \frac{3}{2 3 a + 7} x + 3 a + 7 - \frac{3 a}{2 3 a + 7}

y = \frac{3}{2 3 a + 7} x + 3 a + 7 - \frac{3 a}{2 3 a + 7}

\frac{d}{d y} (\frac{x}{( x + y ) ^{2}})

\frac{d}{d x} (\frac{5 - x}{x})

\int x^{3} - \frac{1}{x ^{2}} - x^{\frac{2}{3}} d x

x \to \infty lim (5 x^{2})

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

What is the tangent of f(x)=sqrt(3x+7),\at a=6 ?
The tangent of f(x)=sqrt(3x+7),\at a=6 is y= 3/(2sqrt(3a+7))x+sqrt(3a+7)-(3a)/(2sqrt(3a+7))