Find the extreme values of the function $\mathrm{f}(\mathrm{x}, \mathrm{y}, \mathrm{z})=8 \mathrm{x} \mathrm{y}+2 \mathrm{z}^{2}$ on the circle in which the plane $\mathrm{y}-\mathrm{x}=0$ intersects the sphere $\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{z}^{2}=49$ The maximum value of $f(x, y, z)$ is At which point(s) does the maximum value of $\mathrm{f}\mathrm{x}, \mathrm{y}, \mathrm{z})$ occur? Select all that apply. A. $\left(0,0, \frac{ \sqrt{2}}{2} ight) B. $C0,0,7)$ C. $\left(\frac{ \sqrt{2}}2}, \frac{7 \sqrt{2}}{2}, ight) D. $\left(\frac{7 \sqrt{2}}2}, - \frac{7 \sqrt{2}}2}, ight) E. $(0,0,-7)$ F. $\left( \frac{7 \sqrt{2}}2}, -\frac{7 \sqrt{2}}{2), ight) G. $\left(0,0,-\frac{ \sqrt{2}}{2} ight)$ H. $\left(-\frac{ \sqrt{2}}2}, \frac{ \sqrt{2}}{2}, ight) SP.SD.420