Find the Absolute Maximum and Minimum Values of the Function $$\text { Function: } f ( x , y ) = x ^ { 2 } + y ^ { 2 } ; \text { curve: } x = 5 t + 1 , y = 5 t - 1,0 \leq t \leq 1 \text {. }$$

Multiple Choice

Find the absolute maximum and minimum values of the function on the given curve.
- $$\text { Function: } f ( x , y ) = x ^ { 2 } + y ^ { 2 } ; \text { curve: } x = 5 t + 1 , y = 5 t - 1,0 \leq t \leq 1 \text {. }$$

A) Absolute maximum: 52 at t = 1; absolute minimum: 2 at t = 0.
B) Absolute maximum: 51 at t = 1; absolute minimum: 6 at t = 0.
C) Absolute maximum: 51 at t = 1; absolute minimum: 2 at t = 0.
D) Absolute maximum: 52 at t = 1; absolute minimum: 6 at t = 0.