What is the tangent of f(x)=sqrt(2x+3) ?

The tangent of f(x)=sqrt(2x+3) is y= 1/(sqrt(2a_{0)+3)}x+sqrt(2a_{0)+3}-(a_{0})/(sqrt(2a_{0)+3)}

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tangent of f(x)=sqrt(2x+3)

tangent of

f (x) = 2 x + 3

y = \frac{1}{2 a _{0} + 3} x + 2 a_{0} + 3 - \frac{a _{0}}{2 a _{0} + 3}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 2 a_{0} + 3)

Find the slope of

f (x) = 2 x + 3 : \frac{df ( x )}{d x} = \frac{1}{2 x + 3}

Compute the slope of

f (x) = 2 x + 3

x = a_{0} : m = \frac{1}{2 a _{0} + 3}

Find the line with slope m=

\frac{1}{2 a _{0} + 3}

and passing through

(a_{0}, 2 a_{0} + 3) : y = \frac{1}{2 a _{0} + 3} x + 2 a_{0} + 3 - \frac{a _{0}}{2 a _{0} + 3}

y = \frac{1}{2 a _{0} + 3} x + 2 a_{0} + 3 - \frac{a _{0}}{2 a _{0} + 3}

\int u^{2} + 1 d u

ln (1 - 9 x)

x \to 1 lim (- \frac{3}{x - 1})

y^{^{'}} = y^{3} - 6 x^{2} y^{3}

\int e^{5 θ} sin (6 θ) d θ

What is the tangent of f(x)=sqrt(2x+3) ?
The tangent of f(x)=sqrt(2x+3) is y= 1/(sqrt(2a_{0)+3)}x+sqrt(2a_{0)+3}-(a_{0})/(sqrt(2a_{0)+3)}