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y=x^(2)+x+1quad[2,3]

$y=x^{2}+x+1 \quad[2,3]$

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Evaluate integers raised to rational exponents

Full solution

Q.

y=x^{2}+x+1 \quad[2,3]

Plug in Lower Bound: Plug in the lower bound of the interval, $x = 2$ , into the function. $\newline$ $y = 2^2 + 2 + 1$ $\newline$ $y = 4 + 2 + 1$ $\newline$ $y = 7$
Plug in Upper Bound: Now plug in the upper bound of the interval, $x = 3$ , into the function. $\newline$ $y = 3^2 + 3 + 1$ $\newline$ $y = 9 + 3 + 1$ $\newline$ $y = 13$
Values on Interval: Since the function is continuous and differentiable on the interval $[2,3]$ , and we are not asked for the maximum or minimum values, the values of the function on this interval will be all the $y$ values between $y(2)$ and $y(3)$ .

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