find-the-X-0-value-of-the-x-variable-with-which-the-function-assumes-the-lower-value-f-x-x-2-3x-7-sin-pix-

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}

Facebook Tweet Pin