Question 1

Which of the following options is true? Edwin plotted a graph on Desmos (an online graphing tool), which was continuous and differentiable at every point. Later he remembered the form of the function $f(x)$ that represents the graph that he plotted but forgot some of the values that appeared in the expression. So he used $m, n,$ and $p$ in place of the missing values and the function he wrote down had the following expression: $$f(x) = \begin{cases} ne^x + 3, & x < 0 \\ mx + 2, & x = 0 \\ 5x + p + 1, & x > 0 \end{cases}$$ Can you help Edwin by finding the values of $m, n,$ and $p$? Which of the following statements is (are) correct?