What is the tangent of f(x)=sqrt(14-x),\at x=5 ?

The tangent of f(x)=sqrt(14-x),\at x=5 is y=-1/6 x+23/6

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tangent of f(x)=sqrt(14-x),\at x=5

tangent of

f (x) = 14 - x, at x = 5

y = - \frac{1}{6} x + \frac{23}{6}

Solution steps

Find the tangent point:

(5, 3)

Find the slope of

f (x) = 14 - x : \frac{df ( x )}{d x} = - \frac{1}{2 14 - x}

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{1}{6}

Find the line with slope m=

- \frac{1}{6}

and passing through

(5, 3) : y = - \frac{1}{6} x + \frac{23}{6}

y = - \frac{1}{6} x + \frac{23}{6}

What is the tangent of f(x)=sqrt(14-x),\at x=5 ?
The tangent of f(x)=sqrt(14-x),\at x=5 is y=-1/6 x+23/6