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

The tangent of f(x)=sqrt(x+7),\at x=-6 is y= 1/2 x+4

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

tangent of

f (x) = x + 7, at x = - 6

y = \frac{1}{2} x + 4

Solution steps

Find the tangent point:

(- 6, 1)

Find the slope of

f (x) = x + 7 : \frac{df ( x )}{d x} = \frac{1}{2 x + 7}

Compute the slope of

f (x) = x + 7

x = - 6 : m = \frac{1}{2}

Find the line with slope m=

\frac{1}{2}

and passing through

(- 6, 1) : y = \frac{1}{2} x + 4

y = \frac{1}{2} x + 4

\frac{d}{d x} (4^{- \frac{x}{4}})

\frac{4 x ^{2} - 3}{8 x ^{3} + 1}

\frac{d}{d x} (\frac{x cos ( π x ) + 1}{1 - x})

\frac{s + 1}{s ^{2} + 2}

(y - x 2) d x + (x + y 2) d y = 0

What is the tangent of f(x)=sqrt(x+7),\at x=-6 ?
The tangent of f(x)=sqrt(x+7),\at x=-6 is y= 1/2 x+4