What is the tangent of f(x)=x+sqrt(x) ?

The tangent of f(x)=x+sqrt(x) is y=(1+1/(2sqrt(a_{0))})x+sqrt(a_{0)}-(sqrt(a_{0)})/2

Popular >

tangent of f(x)=x+sqrt(x)

tangent of

f (x) = x + x

y = (1 + \frac{1}{2 a _{0}}) x + a_{0} - \frac{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} = 1 + \frac{1}{2 x}

Compute the slope of

f (x) = x + x

x = a_{0} : m = 1 + \frac{1}{2 a _{0}}

Find the line with slope m=

1 + \frac{1}{2 a _{0}}

and passing through

(a_{0}, a_{0} + a_{0}) : y = (1 + \frac{1}{2 a _{0}}) x + a_{0} - \frac{a _{0}}{2}

y = (1 + \frac{1}{2 a _{0}}) x + a_{0} - \frac{a _{0}}{2}

\int \frac{- 3}{( x ^{2} + 3 ) ^{\frac{3}{2}}} d x

y = - x^{2} - x, y = 3 x

(\frac{d x}{d y}) = k (a - x) (a - x)

\frac{1}{12 x}

\frac{d}{d x} (5 x - x^{- \frac{1}{3}} - 1)

What is the tangent of f(x)=x+sqrt(x) ?
The tangent of f(x)=x+sqrt(x) is y=(1+1/(2sqrt(a_{0))})x+sqrt(a_{0)}-(sqrt(a_{0)})/2