To find a maximum or minimum value of a function, look for parts of
the expression—especially squares—that have upper or lower limits.Example 3If you have a graphing calculator (and know how to use it), you could graph
the function and trace the graph to find the maximum. But it’s really a lot
easier if you conceptualize the situation. The expression 2 − (x + 2)^2 will be at
its maximum when the part being subtracted from the 2 is as small as it can
be. The part after the minus sign, (x + 2)^2 , is the square of something, so it
must be positive and can be no smaller than 0. When x = −2, (x + 2)^2 = 0, and
the whole expression 2 − (x + 2)^2 = 2 − 0 = 2. For any other value of x, the part
after the minus sign will be greater than 0, and the whole expression will be
less than 2. So 2 is the maximum value, and the answer is (D).
1. What is the maximum value of f(x) = 2 − (x + 2)^2?(A) −4(B) −2(C) 0(D) 2(E) 4