What is the tangent of f(x)=18sqrt(x),\at x=9 ?

The tangent of f(x)=18sqrt(x),\at x=9 is y=3x+27

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tangent of f(x)=18sqrt(x),\at x=9

tangent of

f (x) = 18 x, at x = 9

y = 3 x + 27

Solution steps

Find the tangent point:

(9, 54)

Find the slope of

f (x) = 18 x : \frac{df ( x )}{d x} = \frac{9}{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 = 3

Find the line with slope m=

3

and passing through

(9, 54) : y = 3 x + 27

y = 3 x + 27

What is the tangent of f(x)=18sqrt(x),\at x=9 ?
The tangent of f(x)=18sqrt(x),\at x=9 is y=3x+27