What is the tangent of f(x)=3sin(x),\at x= pi/3 ?

The tangent of f(x)=3sin(x),\at x= pi/3 is y= 3/2 x+(3sqrt(3)-pi)/2

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tangent of f(x)=3sin(x),\at x= pi/3

tangent of

f (x) = 3 sin (x), at x = \frac{π}{3}

y = \frac{3}{2} x + \frac{3 3 - π}{2}

Solution steps

Find the tangent point:

(\frac{π}{3}, \frac{3 3}{2})

Find the slope of

f (x) = 3 sin (x) : \frac{df ( x )}{d x} = 3 cos (x)

Compute the slope of

f (x) = 3 sin (x)

x = \frac{π}{3} : m = \frac{3}{2}

Find the line with slope m=

\frac{3}{2}

and passing through

(\frac{π}{3}, \frac{3 3}{2}) : y = \frac{3}{2} x + \frac{3 3 - π}{2}

y = \frac{3}{2} x + \frac{3 3 - π}{2}

f (x) = 2^{x} ln (2)

y^{^{'}} = y + x^{2}

\frac{d y}{d x} = \frac{x ( e ^{x^{2}} + 2 )}{6 y ^{2}}

y = (6 x - 2) (5 x + 7)

What is the tangent of f(x)=3sin(x),\at x= pi/3 ?
The tangent of f(x)=3sin(x),\at x= pi/3 is y= 3/2 x+(3sqrt(3)-pi)/2