find the X_0 value of the x variable with which the function assumes the lower value. f(x)=x^2 −3x+7+sin(πx)


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Question Number 56500 by kelly33 last updated on 17/Mar/19

$f i n d t h e X_{0} v a l u e o f t h e x v a r i a b l e w i t h w h i c h$ $t h e f u n c t i o n a s s u m e s t h e l o w e r v a l u e .$ $f (x) = x^{2} - 3 x + 7 + s i n (π x)$
Commented by kelly33 last updated on 17/Mar/19

$p l z h e l p m e$
	Answered by tanmay.chaudhury50@gmail.com last updated on 17/Mar/19

	$f (x) = x^{2} - 3 x + 7 + s i n (π x)$ $= x^{2} - 2 . x . \frac{3}{2} + \frac{9}{4} + 7 - \frac{9}{4} + s i n π x$ $= {(x - \frac{3}{2})}^{2} + \frac{19}{4} + s i n (π x)$ $f o r m i n v a l u e {(x - \frac{3}{2})}^{2} = 0$ $x = \frac{3}{2} \to s i n (\frac{3 π}{2}) = - 1$ $s o m i n v a l u e i s \frac{19}{4} - 1 = \frac{15}{4} = 3.75$
	Commented by tanmay.chaudhury50@gmail.com last updated on 17/Mar/19

	Commented by kelly33 last updated on 19/Mar/19

	$= x^{2} - 2 . x . \frac{3}{2} + \frac{9}{4} + 7 - \frac{9}{4} + s i n π x$ $= {(x - \frac{3}{2})}^{2} + \frac{19}{4} + s i n (π x)$ $w h e r e d i d t h i s c o m e f r o m ?$
	Commented by tanmay.chaudhury50@gmail.com last updated on 19/Mar/19

	$l e a r n b a s i c m a t h t h e n a t t e m t h a r d p r o b l e m . .$ $f o r m u l a {(a + b)}^{2} = a^{2} + 2 a b + b^{2}$ $n o w$ $4 a^{2} + 4 a + 1$ ${(2 a)}^{2} + 2.2 a . 1 + {(1)}^{2}$ ${(2 a + 1)}^{2}$ $a^{2} - 3 a + 2$ ${(a)}^{2} - 2 \times a \times \frac{3}{2} + {(\frac{3}{2})}^{2} - \frac{9}{4} + 2$ ${(a - \frac{3}{2})}^{2} - \frac{1}{4}$ $s i m i l a r l y$ $x^{2} - 3 x + 7$ ${(x)}^{2} - 2 \times x \times \frac{3}{2} + {(\frac{3}{2})}^{2} + 7 - \frac{9}{4}$ ${(x - \frac{3}{2})}^{2} + \frac{19}{4}$
	Commented by kelly33 last updated on 19/Mar/19

	$w h e r e e m e r g e d \frac{3}{2} a n d \frac{- 9}{4}$
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