The range in which y = -x^{2} + 6x - 3 is inc | vedclass

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(A) Given the function $y = -x^{2} + 6x - 3$. To find the interval where the function is increasing,we calculate the first derivative: $\frac{dy}{dx}

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$x < 3$

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(A) Given the function $y = -x^{2} + 6x - 3$. To find the interval where the function is increasing,we calculate the first derivative: $\frac{dy}{dx} = -2x + 6$. $A$ function is increasing when its derivative is greater than zero,i.e.,$\frac{dy}{dx} > 0$. Setting the derivative greater than zero: $-2x + 6 > 0$. Subtracting $6$ from both sides: $-2x > -6$. Dividing by $-2$ (and reversing the inequality sign): $x Therefore,the function is increasing in the range $x < 3$.

The range in which $y = -x^{2} + 6x - 3$ is increasing is

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