What is the tangent of-x^2+4(sqrt(x)) ?

The tangent of-x^2+4(sqrt(x)) is y=(-2a_{0}+2/(sqrt(a_{0))})x+a_{0}^2+2sqrt(a_{0)}

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tangent of-x^2+4(sqrt(x))

tangent of

- x^{2} + 4 (x)

y = (- 2 a_{0} + \frac{2}{a _{0}}) x + a_{0}^{2} + 2 a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, - a_{0}^{2} + 4 a_{0})

Find the slope of

y = - x^{2} + 4 x : \frac{d y}{d x} = - 2 x + \frac{2}{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 = - 2 a_{0} + \frac{2}{a _{0}}

Find the line with slope m=

- 2 a_{0} + \frac{2}{a _{0}}

and passing through

(a_{0}, - a_{0}^{2} + 4 a_{0}) : y = (- 2 a_{0} + \frac{2}{a _{0}}) x + a_{0}^{2} + 2 a_{0}

y = (- 2 a_{0} + \frac{2}{a _{0}}) x + a_{0}^{2} + 2 a_{0}

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What is the tangent of-x^2+4(sqrt(x)) ?
The tangent of-x^2+4(sqrt(x)) is y=(-2a_{0}+2/(sqrt(a_{0))})x+a_{0}^2+2sqrt(a_{0)}