F(x) = -x^4 + 8x^2 + 8*

fx-x4-8x2-8

#1

F(x) = -x^4 + 8x^2 + 8

(a) Determine whether F is even, odd, or neither.
(b) There is a local maximum value of 24 at x = 2. Determine a second local maximum value.
© Suppose the area under the graph of F between x = 0 and x = 3 that is bounded from below by the x-axis is 47.4 square units. Using the result from part (a), determine the area under the graph of F between x = -3 and x = 0 that is bounded from below by the x-axis.

Answer:

a) F(-x) = -(-x)^4 + 8 (-x)^2 + 8 = -x^4 + 8x^2 + 8 = F(x). So, F(x) is even
b) There is a local maximum value of 24 at x = 2 and F(x) is even. So, the graph of F(x) is symmetric about the y-axis. Therefore, the second local maximum value is 24 at x = -2
c) F(x) is even. So, the graph of F(x) is symmetric about the y-axis. Therefore, the area under the graph of F between x = -3 and x = 0 that is bounded from below by the x-axis is 47.4 square units too.