Question

Find the slope of the curve f(x) = cos(3x) at π/4

Answer 1

`f(x)=\cos(3x)\\ f'(x)=-\sin(3x)\cdot 3=-3\sin (3x)\\ f'\left((\pi)/(4)\right)=-3\sin\left(3\cdot(\pi)/(4)\right)\\ f'\left((\pi)/(4)\right)=-3\cdot(\sqrt2)/(2)\\ f'\left((\pi)/(4)\right)=-(3\sqrt2)/(2)\\`

So the slope is
`-(3\sqrt2)/(2)`