What is the tangent of 18sqrt(x)-3x ?

The tangent of 18sqrt(x)-3x is y=(9/(sqrt(a_{0))}-3)x+9sqrt(a_{0)}

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tangent of 18sqrt(x)-3x

tangent of

18 x - 3 x

y = (\frac{9}{a _{0}} - 3) x + 9 a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 18 a_{0} - 3 a_{0})

Find the slope of

y = 18 x - 3 x : \frac{d y}{d x} = \frac{9}{x} - 3

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{9}{a _{0}} - 3

Find the line with slope m=

\frac{9}{a _{0}} - 3

and passing through

(a_{0}, 18 a_{0} - 3 a_{0}) : y = (\frac{9}{a _{0}} - 3) x + 9 a_{0}

y = (\frac{9}{a _{0}} - 3) x + 9 a_{0}

What is the tangent of 18sqrt(x)-3x ?
The tangent of 18sqrt(x)-3x is y=(9/(sqrt(a_{0))}-3)x+9sqrt(a_{0)}