Question

The expression 2x^2+4x+7 has minimum value m at x=alpha,then the value of m and alpha are.
a)5,1
b)-5,-l
c)-5,1
d)5,-1

Answer 1

Given :  The expression 2x^2+4x+7 has minimum value m at x=alpha

To Find :  value of m and alpha

Solution:

2x² + 4x + 7

= 2x² + 4x + 2 + 5

= 2(x² + 2x + 1) + 5

= 2(x + 1)² + 5

Minimum value of (x + 1)²  is 0

when x + 1 = 0

=> x = - 1

=> α = -1

and minimum value

m = 2 (-1 + 1)² + 5

=> m = 5

m = 5

α = -1

Option d ) 5 , - 1 is correct

or using maxima & minima

Z  = 2x² + 4x + 7

dZ/dx = 4x + 4

dZ/dx =  0 => 4x + 4 = 0  => x = - 1

d²Z/dx²  = 4  > 0 hence value is minimum at x = - 1

Z = 2(-1)² + 4(-1) + 7 = 5

minimum value = 5

Learn  More:

The minimum value of the expression (3b+4c)/a + (4c+a)

https://brainly.in/question/13230728

find minimum value of x^2+y^2+z^2,given that xyz=a^3

https://brainly.in/question/1876026

Answer 2

Answer:

value of m and alpha is 5,-1