What is the tangent of 24sqrt(x)-4x ?

The tangent of 24sqrt(x)-4x is y=((12)/(sqrt(a_{0))}-4)x+12sqrt(a_{0)}

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tangent of 24sqrt(x)-4x

tangent of

24 x - 4 x

y = (\frac{12}{a _{0}} - 4) x + 12 a_{0}

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 24 a_{0} - 4 a_{0})

Find the slope of

y = 24 x - 4 x : \frac{d y}{d x} = \frac{12}{x} - 4

Compute the slope of

y = 24 x - 4 x

x = a_{0} : m = \frac{12}{a _{0}} - 4

Find the line with slope m=

\frac{12}{a _{0}} - 4

and passing through

(a_{0}, 24 a_{0} - 4 a_{0}) : y = (\frac{12}{a _{0}} - 4) x + 12 a_{0}

y = (\frac{12}{a _{0}} - 4) x + 12 a_{0}

\frac{d y}{d x} = \frac{1}{2} x + 1

f (x) = \frac{1}{x}, g (x) = \frac{1}{3}, [2, 5]

\frac{7 u ^{2}}{( u ^{2} + u ) ^{3}}

\int \frac{3 x ^{2}}{1 - x ^{6}} d x

x, x^{2} - 2

What is the tangent of 24sqrt(x)-4x ?
The tangent of 24sqrt(x)-4x is y=((12)/(sqrt(a_{0))}-4)x+12sqrt(a_{0)}