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

The tangent of f(x)=sqrt(5x+6),\at x=2 is y= 5/8 x+11/4

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

tangent of

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

y = \frac{5}{8} x + \frac{11}{4}

Solution steps

Find the tangent point:

(2, 4)

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 = 2 : m = \frac{5}{8}

Find the line with slope m=

\frac{5}{8}

and passing through

(2, 4) : y = \frac{5}{8} x + \frac{11}{4}

y = \frac{5}{8} x + \frac{11}{4}

x \frac{d y}{d x} + 2 y = 8 x^{2}

n = 0 \sum \infty \frac{5}{4 ^{n}}

\int ln (6 x + 7) d x

(1 + cos (t)) y^{^{'}} = (1 - e^{- y}) sin (t)

\int x^{2} (x^{3} - 4)^{3} d x

What is the tangent of f(x)=sqrt(5x+6),\at x=2 ?
The tangent of f(x)=sqrt(5x+6),\at x=2 is y= 5/8 x+11/4