- #1
songoku
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- Homework Statement
- For ##f(x)=x^2+|x-a|+1, x ~\text{and} ~a \in \mathbb{R} ##, find minimum value of ##f(x)## in terms of ##a##
- Relevant Equations
- Modulus Function
(1) For ##x>a##
##f(x)=x^2+x-a+1 \rightarrow## minimum value obtained when ##x=-\frac{1}{2}##
Minimum value of ##f(x)=\frac{3}{4} -a##
(2) For ##x<a##
##f(x)=x^2-x+a+1 \rightarrow## minimum value obtained when ##x=\frac{1}{2}##
Minimum value of ##f(x)=\frac{3}{4}+a##
But the teacher said there is missing solution (my final answer is not complete yet). I don't understand which one it is
Thanks
##f(x)=x^2+x-a+1 \rightarrow## minimum value obtained when ##x=-\frac{1}{2}##
Minimum value of ##f(x)=\frac{3}{4} -a##
(2) For ##x<a##
##f(x)=x^2-x+a+1 \rightarrow## minimum value obtained when ##x=\frac{1}{2}##
Minimum value of ##f(x)=\frac{3}{4}+a##
But the teacher said there is missing solution (my final answer is not complete yet). I don't understand which one it is
Thanks