Consider the objective function $Z=x-y$ subject to the constraints

$$ \begin{aligned} & x+2 y \leq 10 \\ & x+y \geq 2 \\ & x \geq 0, y \geq 0 \end{aligned} $$

What is the minimum value of $Z$ subject to the above constraints?

42. Let $p(x)=x^2+b x+c$ be quadratic polynomial with real coefficients $b$ and $c$. Suppose $p(1)=5$ and $p(-1)=3$. What is the product of the roots of $p(x)=0$ ?

Let $f:(-1,2) \rightarrow \mathbf{R}$ be a differentiable function such that $f^{\prime}(x)=\frac{2}{x^2-5}$ and $f(0)=0$. Then in which of the following intervals does $f(1)$ lie?

Let $f(x)=\sin (3 x), x \in\left[0, \frac{\pi}{2}\right]$. Which of the following statements is true