What is the tangent of f(x)=sqrt(x^2+11),\at x=5 ?

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

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tangent of f(x)=sqrt(x^2+11),\at x=5

tangent of

f (x) = x^{2} + 11, at x = 5

y = \frac{5}{6} x + \frac{11}{6}

Solution steps

Find the tangent point:

(5, 6)

Find the slope of

f (x) = x^{2} + 11 : \frac{df ( x )}{d x} = \frac{x}{x ^{2} + 11}

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{5}{6}

Find the line with slope m=

\frac{5}{6}

and passing through

(5, 6) : y = \frac{5}{6} x + \frac{11}{6}

y = \frac{5}{6} x + \frac{11}{6}

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