Answer
a. F is even.
b. Local maximum of $24$ at $x=−2$
c. $A=474\ sq.units$
Work Step by Step
a.
$F(−x)=−(−x)^4+8(−x)^2+8=−x^4+8x^2+8=F(x)$
$F(−x)=F(x)$, so the function is even.
b.
Being even, its graph has y-axis symmetry.
If $(2,24)$ is a local maximum point, then the point symmetric to it,
$(−2,24)$ is on the graph and is also a local maximum point.
c.
Because of symmetry relative to the y-axis, the area enclosed
between $x=3$ and the y-axis
equals the area enclosed from the y-axis to $x= -3$
$A=474\ sq.units$
