Consider the function f(x) = x^4 - 72 x^2 + 3, -5 less than or equal to x less than or equal to 13. This function has an absolute minimum value equal to and an absolute maximum value to

Question

Consider the function f(x) = x^4 - 72 x^2  + 3, -5 less than or equal to x less than or equal to 13. This function has an absolute minimum value equal to and an absolute maximum value to

Reiny · Answer

f ' (x) = 4x^3 - 144x
= 0 at any local max/min

4x(x^2 - 36) = 0
x = 0 , -6, +6

f(0) = 3
f(6) = -1293
f(-6) = -1293

checking for endpoint of domain
f(-5) = -1172
f(13) = 16396

so absolute min = -1293
absolute max = 16396

looks good,
http://www.wolframalpha.com/input/?i=plot++x%5E4+-+72+x%5E2+%2B+3%2C+-5+≤+x+≤+13