What is the tangent of y=3x+6cos(x),\at (pi/3) ?

The tangent of y=3x+6cos(x),\at (pi/3) is y=(3-6sin(a_{0}))x+6a_{0}sin(a_{0})+6cos(a_{0})

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tangent of y=3x+6cos(x),\at (pi/3)

tangent of

y = 3 x + 6 cos (x), at (\frac{π}{3})

y = (3 - 6 sin (a_{0})) x + 6 a_{0} sin (a_{0}) + 6 cos (a_{0})

Solution steps

Compute the tangent line to the general point

x = a_{0}

Find the tangent point:

(a_{0}, 3 a_{0} + 6 cos (a_{0}))

Find the slope of

y = 3 x + 6 cos (x) : \frac{d y}{d x} = 3 - 6 sin (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 = 3 - 6 sin (a_{0})

Find the line with slope m=

3 - 6 sin (a_{0})

and passing through

(a_{0}, 3 a_{0} + 6 cos (a_{0})) : y = (3 - 6 sin (a_{0})) x + 6 a_{0} sin (a_{0}) + 6 cos (a_{0})

y = (3 - 6 sin (a_{0})) x + 6 a_{0} sin (a_{0}) + 6 cos (a_{0})

\frac{s}{s ^{2} + 2 s + 3}

f (x) = \frac{2 x ^{3} - 3 x + 1}{x}

y = x^{2} - 2

e^{- t} (t^{2})

f (x) = x + 7 x

What is the tangent of y=3x+6cos(x),\at (pi/3) ?
The tangent of y=3x+6cos(x),\at (pi/3) is y=(3-6sin(a_{0}))x+6a_{0}sin(a_{0})+6cos(a_{0})