Assertion (A): The maximum value of -x^2+3x+1 | vedclass

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(D) Assertion $(A)$: Let $f(x) = -x^2+3x+1$.To find the maximum value,we find the critical point by setting $f'(x) = 0$.$f'(x) = -2x+3 = 0 \Rightarrow

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$(A)$ is false but $(R)$ is true

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(D) Assertion $(A)$: Let $f(x) = -x^2+3x+1$.To find the maximum value,we find the critical point by setting $f'(x) = 0$.$f'(x) = -2x+3 = 0 \Rightarrow x = \frac{3}{2}$.Since $f''(x) = -2 The maximum value is $f\left(\frac{3}{2}\right) = -\left(\frac{3}{2}\right)^2 + 3\left(\frac{3}{2}\right) + 1 = -\frac{9}{4} + \frac{9}{2} + 1 = \frac{-9+18+4}{4} = \frac{13}{4}$.Since the given assertion states the maximum value is $\frac{11}{4}$,the assertion $(A)$ is false.Reason $(R)$: For $f(x) = ax^2+bx+c$ with $a $f'(x) = 2ax+b = 0 \Rightarrow x = -\frac{b}{2a}$.Since $f''(x) = 2a Thus,the reason $(R)$ is true.

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

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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