Find the point on the curve $y=x^{3}-11x+5$ at which the tangent is $y=x-11$.

If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes an angle $\left(\frac{3 \pi}{4}\right)^{C}$ with the positive $X$-axis,then $f^{\prime}(3)$ is equal to

If the tangent to the curve $y=x^{3}-x^{2}+x$ at the point $(a, b)$ is also tangent to the curve $y=5x^{2}+2x-25$ at the point $(2, -1)$,then $|2a+9b|$ is equal to $........$

The angle between the curves $y=\sin x$ and $y=\cos x$ is

The tangent to the curve $y = 2x^2 - x + 1$ at a point $P$ is parallel to the line $y = 3x + 4$. The coordinates of $P$ are:

The values of parameter $a$ such that the line $(\log_{2}(1 + 5a - a^{2}))x - 5y - (a^{2} - 5) = 0$ is a normal to the curve $xy = 1$ may lie in the interval