The maximum value of the function $f(x) = x^{3} - 12x^{2} + 36x + 17$ in the interval $[1, 10]$ is:

Let $f(x)=1+\frac{x}{1 !}+\frac{x^2}{2 !}+\frac{x^3}{3 !}+\frac{x^4}{4 !}$. The number of real roots of $f(x)=0$ is

At what value of $x$ is the function $f(x) = x(1 - x^2)$ maximum for $0 \leq x \leq 2$?

The maximum value $M$ of $f(x) = 3^x + 5^x - 9^x + 15^x - 25^x$,as $x$ varies over all real numbers,satisfies:

The sum of all the local minimum values of the twice differentiable function $f: R \rightarrow R$ defined by $f(x)=x^{3}-3 x^{2}-\frac{3 f^{\prime \prime}(2)}{2} x+f^{\prime \prime}(1)$ is:

The maximum area of a triangle whose one vertex is at $(0,0)$ and the other two vertices lie on the curve $y = -2x^2 + 54$ at points $(x, y)$ and $(-x, y)$ where $y > 0$ is: