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

The tangent of f(x)=cos(x),\at x= pi/4 is y=-(sqrt(2))/2 x+1/(sqrt(2))+pi/(4sqrt(2))

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

tangent of

f (x) = cos (x), at x = \frac{π}{4}

y = - \frac{2}{2} x + \frac{1}{2} + \frac{π}{4 2}

Solution steps

Find the tangent point:

(\frac{π}{4}, \frac{2}{2})

Find the slope of

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

Find the line with slope m=

- \frac{2}{2}

and passing through

(\frac{π}{4}, \frac{2}{2}) : y = - \frac{2}{2} x + \frac{1}{2} + \frac{π}{4 2}

y = - \frac{2}{2} x + \frac{1}{2} + \frac{π}{4 2}

What is the tangent of f(x)=cos(x),\at x= pi/4 ?
The tangent of f(x)=cos(x),\at x= pi/4 is y=-(sqrt(2))/2 x+1/(sqrt(2))+pi/(4sqrt(2))