Practice using the extreme value theorem.

Problem

Consider the function
space, f, left parenthesis, x, right parenthesis, equals, sine, start superscript, 2, end superscript, x, minus, cosine, start superscript, 2, end superscript, x
on the closed interval x[π4,3π4]x\in\left[\dfrac{\pi}{4},\dfrac{3\pi}{4}\right].
If f, left parenthesis, c, right parenthesis is the absolute maximum value of f, what is c, space? What is f, left parenthesis, c, right parenthesis?
c, equals
  • Your answer should be
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i
f, left parenthesis, c, right parenthesis, equals
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
Get 3 answers correct in a row