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

The function $f(x) = \int \dfrac{x+3}{x^2-9x+20}\,dx$, then $f(x)$ is

If $f(x) = \log(1 + x) - \dfrac{x}{1+x}$, then the values of $x$ for which $f(x)$ is monotonically increasing and monotonically decreasing are respectively.....