What is the tangent of f(x)=xsqrt(x) ?

The tangent of f(x)=xsqrt(x) is y=(3sqrt(a_{0)})/2 x+a_{0}sqrt(a_{0)}-(3a_{0}sqrt(a_{0)})/2

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tangent of f(x)=xsqrt(x)

tangent of

f (x) = x x

y = \frac{3 a _{0}}{2} x + a_{0} a_{0} - \frac{3 a _{0} a _{0}}{2}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, a_{0} a_{0})

Find the slope of

f (x) = x x : \frac{df ( x )}{d x} = \frac{3 x}{2}

Compute the slope of

f (x) = x x

x = a_{0} : m = \frac{3 a _{0}}{2}

Find the line with slope m=

\frac{3 a _{0}}{2}

and passing through

(a_{0}, a_{0} a_{0}) : y = \frac{3 a _{0}}{2} x + a_{0} a_{0} - \frac{3 a _{0} a _{0}}{2}

y = \frac{3 a _{0}}{2} x + a_{0} a_{0} - \frac{3 a _{0} a _{0}}{2}

(4 x^{2} + 2 x y) \frac{d y}{d x} + (12 x y + 2 y^{2}) = 0

\int_{\frac{1}{2}}^{1} sin (2 π x) d x

y = - x^{2} + 4, y = 2 x + 1

500000 + 5000 t^{2}

\frac{d}{d x} (\frac{( 3 x + 5 )}{( 2 x - 6 )})

What is the tangent of f(x)=xsqrt(x) ?
The tangent of f(x)=xsqrt(x) is y=(3sqrt(a_{0)})/2 x+a_{0}sqrt(a_{0)}-(3a_{0}sqrt(a_{0)})/2