If the normal to the curve $$y = f\left( x \right)$$ and the point $$(3, 4)$$ makes an angle $${{{3\pi } \over 4}}$$ with the positive $$x$$-axis, then $$f'\left( 3 \right) = $$

The function $$f(x)=$$ $${\sin ^4}x + {\cos ^4}x$$ increases if

If $$f\left( x \right) = {{{x^2} - 1} \over {{x^2} + 1}},$$ for every real number $$x$$, then the minimum value of $$f$$

The number of values of $$x$$ where the function
$$f\left( x \right) = \cos x + \cos \left( {\sqrt 2 x} \right)$$ attains its maximum is