What is the tangent of f(x)=2cos(3x),\at x= pi/2 ?

The tangent of f(x)=2cos(3x),\at x= pi/2 is y=6x-3pi

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tangent of f(x)=2cos(3x),\at x= pi/2

tangent of

f (x) = 2 cos (3 x), at x = \frac{π}{2}

y = 6 x - 3 π

Solution steps

Find the tangent point:

(\frac{π}{2}, 0)

Find the slope of

f (x) = 2 cos (3 x) : \frac{df ( x )}{d x} = - 6 sin (3 x)

Compute the slope of

f (x) = 2 cos (3 x)

x = \frac{π}{2} : m = 6

Find the line with slope m=

6

and passing through

(\frac{π}{2}, 0) : y = 6 x - 3 π

y = 6 x - 3 π

y = \frac{1}{2} x^{2}, (- 1, - 1)

\frac{d y}{d t} + 3 y = 1

\int_{0}^{2} 4 x^{7} d x

7^{9 x}

What is the tangent of f(x)=2cos(3x),\at x= pi/2 ?
The tangent of f(x)=2cos(3x),\at x= pi/2 is y=6x-3pi