My mother died on December 24, 2017. I sold some of her mutual funds on December 28, 2017 for a capital loss. Can this loss be used in her 2017 income tax return.

This sale after you mother's death is not reportable on the mother's final personal income tax return.  If the account became part of your mother's probate estate as would be the case if the account was not a Transfer on Death account or jointly owned, the sale is reportable on an estate income tax return (Form 1041) of your mother's estate if the estate has more than $600 of gross income (including the proceeds of the mutual-fund sale) during the estate's tax-year.  The investment received a step-up or step-down in basis to the FMV on the date of death, so the change in value in the 4 days following your mother's death might not result in a significant amount of taxable income.

The assumption here is that the mutual funds were not held in a qualified retirement account, otherwise the treatment is quite different.