The coordinates of the points on the curve $4y = x^2$ that are nearest to the point $(0,5)$ are ...

The equation of the tangent to the curve $y = \sqrt{9 - 3x^2}$ at the point where the ordinate and abscissa equal is...

If the line $y = 4x - 5$ is tangent to the curve $y^2 = ax^3 + b$ at the point $(2,3)$, then the value of $7a - 2b$ is...

The derivative of the function $f(x) = \cos^4 x + \sin^4 x,\ 0 \leq x \leq 2\pi$ is positive for