swati007 wrote:
If b=a+4, then for which of the following values of x is the expression (x−a)^2+(x−b)^2 the smallest?
A) a−1
B) a
C) a+2
D) a+3
E) a+5
I know that we can solve this question by plugging in the option values. I want to know the smart way to choose which option to plug in first.
Whenever question asks to find the minimum or maximum possible value of x , given the equation in terms of x , it is always a better approach to differentiate the equation and equate the newly formed equation with zero and now solve for x . You will easily get the required value of x.
For example, in above equation, derivative of (x-a)^2 is 2(x-a), similarly derivative of (x-b)^2 is 2(x-b). Now simply add them and equate to zero. Substitute b in terms of a and get the answer of x.