What is the tangent of f(x)=2sqrt(x)+4/x ,\at x=4 ?

The tangent of f(x)=2sqrt(x)+4/x ,\at x=4 is y= 1/4 x+4

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tangent of f(x)=2sqrt(x)+4/x ,\at x=4

tangent of

f (x) = 2 x + \frac{4}{x}, at x = 4

y = \frac{1}{4} x + 4

Solution steps

Find the tangent point:

(4, 5)

Find the slope of

f (x) = 2 x + \frac{4}{x} : \frac{df ( x )}{d x} = \frac{x ^{\frac{3}{2}} - 4}{x ^{\frac{3}{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 = \frac{1}{4}

Find the line with slope m=

\frac{1}{4}

and passing through

(4, 5) : y = \frac{1}{4} x + 4

y = \frac{1}{4} x + 4

\frac{d}{d x} (\frac{16 x}{x ^{2} + 16})

g (x) = \frac{8}{x + 2}

\int \frac{2}{π} x d x

(cos (x) sin (x) - x y^{2}) d x + y (1 - x^{2}) d y = 0

sin (2 θ)

What is the tangent of f(x)=2sqrt(x)+4/x ,\at x=4 ?
The tangent of f(x)=2sqrt(x)+4/x ,\at x=4 is y= 1/4 x+4