Verified answer

If you need an explination:

take the derivatige of g(x)

g ' (x)= 8- 2x

and set it equal to zero.

8-2x=0

2x=8

x=4

this is a critical number. now evaluate the graph of g(x) in relation to g ' (x)

g ' (x) ____3___4____5 <--- number lines help

sign of g ' (x) _____+________-

f(x).......................... inc........ .......... dec

g ' (3)= 8-2(3)= 2 (positive)

g ' (5)= 8-2(5)= -2 (negative)

g ' (x) is positive before 4, and negative after, which means g(x) is increasing before 4 and decreasing after 4, making x=4 a maximum.

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RE:

Find global maximum and minimum values of the function g(x) = 8 x − x^(2) − 10 if its domain is allreal #s

It has no minimum, as it's graph is a downward opening parabola. It's max is at the vertex, or where f'(x) = 0 if you're in calculus.