find-p-if-y-1-px-3x-2-if-the-maximum-is-13-help-pls-

Question Number 156584 by Ghaniy last updated on 12/Oct/21

find p if y = 1 - px - {3 x}^{2}

if the maximum is 13 (help pls)

Commented by john_santu last updated on 14/Oct/21

m a x f (x) = - 3 x^{2} - p x + 1

w h e n x = - (\frac{- p}{2 (- 3)}) = - \frac{p}{6}

s o \Rightarrow 13 = 1 - p (- \frac{p}{6}) - 3 (\frac{p^{2}}{36})

\Rightarrow 12 = \frac{p^{2}}{6} - \frac{p^{2}}{12}

\Rightarrow 12 = \frac{p^{2}}{12} \Rightarrow p = \pm 12

Answered by mr W last updated on 13/Oct/21

y = 1 - p x - 3 x^{2}

y = 1 - 3 (\frac{p}{3} x + x^{2})

y = 1 - 3 (2 \frac{p}{6} x + x^{2})

y = 1 + \frac{p^{2}}{12} - 3 (\frac{p^{2}}{36} + 2 \frac{p}{6} x + x^{2})

y = 1 + \frac{p^{2}}{12} - 3 {(x + \frac{p}{6})}^{2} ⩽ 1 + \frac{p^{2}}{12}

y_{m a x} = 1 + \frac{p^{2}}{12} = 13

p^{2} = 12^{2}

\Rightarrow p = \pm 12

Commented by otchereabdullai@gmail.com last updated on 13/Oct/21

nice question + nice solution

Commented by Ghaniy last updated on 14/Oct/21

Thank you sir Mr W

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