Find the maximum or minimum value of the Q.Ei) 2x-7-5x2 ii) 3x2+2x+11

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Find the maximum or minimum value of the Q.E

i) $2 x - 7 - 5 x^{2}$ $i i) 3 x^{2} + 2 x + 11$

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Detailed Solution

i) $2 x - 7 - 5 x^{2}$

Given equation $2 x - 7 - 5 x^{2}$

Compare with $a x^{2} + b x + c$ we get

$a = - 5 < 0, b = 2, c = - 7$

If $a < 0$ the given expression is maximum value
Maximum value

$= \frac{4 a c - b^{2}}{4 a} = \frac{4 (- 5) (- 7) - {(2)}^{2}}{4 (- 5)} = \frac{140 - 4}{- 20} = \frac{- 136}{20} = \frac{- 34}{5}$

ii) Given $3 x^{2} + 2 x + 11, a = 3 > 0, b = 2, c = 11$

If $a > 0$ the given expression is maximum value Minimum value

Minimum value $= \frac{4 a c - b^{2}}{4 a}$

$= \frac{4 (3) (11) - {(2)}^{2}}{4 (3)} = \frac{132 - 4}{12} = \frac{128}{12} = \frac{32}{3}$

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