Assertion $(A)$: The maximum value of $-x^2+3x+1$ is $\frac{13}{4}$.
Reason $(R)$: If $a < 0$,the maximum value of $ax^2+bx+c$ exists at $x = -\frac{b}{2a}$.
The correct option among the following is

• A
  $(A)$ is true,$(R)$ is true and $(R)$ is the correct explanation for $(A)$
• B
  $(A)$ is true,$(R)$ is true but $(R)$ is not the correct explanation for $(A)$
• C
  $(A)$ is true but $(R)$ is false
• D
  $(A)$ is false but $(R)$ is true