The question is attached above.

Asked by sudhanshubhushanroy | 19th Nov, 2017, 09:12: PM

Expert Answer:

begin mathsize 16px style To space find space the space minimum space value space of space the space given space function
Use space minima space of space the space function.
straight f left parenthesis straight x right parenthesis equals open parentheses 1 plus straight b squared close parentheses straight x squared plus 2 bx plus 1
straight f apostrophe left parenthesis straight x right parenthesis equals open parentheses 1 plus straight b squared close parentheses 2 straight x plus 2 straight b
straight f apostrophe left parenthesis straight x right parenthesis equals 0
rightwards double arrow straight x equals fraction numerator negative straight b over denominator 1 plus straight b squared end fraction
straight f apostrophe apostrophe left parenthesis straight x right parenthesis equals 2 open parentheses 1 plus straight b squared close parentheses greater than 0
rightwards double arrow 1 plus straight b squared greater than 0
rightwards double arrow straight b squared greater than negative 1
Function space has space minima.
After space putting space this space value space in space the space function
you space get space minimum space value space is space fraction numerator 1 over denominator 1 plus straight b squared end fraction greater than 0
rightwards double arrow 1 plus straight b squared greater or equal than 1
rightwards double arrow fraction numerator 1 over denominator 1 plus straight b squared end fraction less or equal than 1
Hence comma space range space of space straight m left parenthesis straight b right parenthesis space is space left parenthesis 0 comma 1 right square bracket end style

Answered by Sneha shidid | 30th Nov, 2017, 10:46: AM