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

question 65

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.

---

Definitions:

Smallest Observation

The lowest value recorded in a data set.

1st Quartile

The value below which 25% of the data points in a dataset fall, indicating the lower quarter of the data.

3rd Quartile

Also known as the upper quartile, it is the value below which 75% of the data in a dataset falls.

Symmetric Distribution

A distribution where the left and right sides of the distribution are mirror images of each other.