Find the exact location of all the relative and absolute extrema of the function.

Question

g(x) = 2x³ − 6x + 3 with domain [−2, 2]



Answer 1

take the derivative and set equal to zero, solve for x

6x^2 -6 = 0

x = + or - 1

f(1) = -1 the point (1,-1)

f(-1) = 7 the point (-1,7)

that's the relative min and max

then try the end points

f(2) = 7 the point (2,7)

f(-2) = -1, the point (-2,-1)

the relative extrema are also tied for being the absolute extrema, -1 and 7 in that limited interval