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

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

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tangent of f(x)=(x+2sin(x))

tangent of

f (x) = (x + 2 sin (x))

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

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

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

Find the slope of

f (x) = (x + 2 sin (x)) : \frac{df ( x )}{d x} = 1 + 2 cos (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 = 1 + 2 cos (a_{0})

Find the line with slope m=

1 + 2 cos (a_{0})

and passing through

(a_{0}, a_{0} + 2 sin (a_{0})) : y = (1 + 2 cos (a_{0})) x - 2 a_{0} cos (a_{0}) + 2 sin (a_{0})

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

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