What is the tangent of f(x)=4sec(x),\at x= pi/6 ?

The tangent of f(x)=4sec(x),\at x= pi/6 is y= 8/3 x+8/(sqrt(3))-(4pi)/9

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tangent of f(x)=4sec(x),\at x= pi/6

tangent of

f (x) = 4 sec (x), at x = \frac{π}{6}

y = \frac{8}{3} x + \frac{8}{3} - \frac{4 π}{9}

Solution steps

Find the tangent point:

(\frac{π}{6}, \frac{8}{3})

Find the slope of

f (x) = 4 sec (x) : \frac{df ( x )}{d x} = 4 sec (x) tan (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{8}{3}

Find the line with slope m=

\frac{8}{3}

and passing through

(\frac{π}{6}, \frac{8}{3}) : y = \frac{8}{3} x + \frac{8}{3} - \frac{4 π}{9}

y = \frac{8}{3} x + \frac{8}{3} - \frac{4 π}{9}

(2 y^{2} x + 3 x) d x + (2 x^{2} y) d y = 0

\frac{\partial}{\partial v} (\frac{v ^{2}}{u})

\frac{d}{d x} (2 - x - y + 1)

x \to 1 lim (1 + x^{2})

\frac{d}{d x} (100)

What is the tangent of f(x)=4sec(x),\at x= pi/6 ?
The tangent of f(x)=4sec(x),\at x= pi/6 is y= 8/3 x+8/(sqrt(3))-(4pi)/9