First find the derivative of f(x), which is
f'(x) = -4x³-6x+1
Solve for the zeroes of this function, of which 2 are complex. The real zero is at
x = 0.16374000103666. Thus the function has only one maximum, at x=0.16374...
Substitute into the original equation to get
f(0.16374000103666) = 7.082588818868268
Thus the range of f(x) is
(-&infin,7.082588818868268] approximately.
You can see the graph of the function at
http://i263.photobucket.com/albums/ii157/mathmate/Danny.png
Find the maximum value of the function f(x)=-x4-3x2+x+7 and use it to determine the range of f.
1 answer
1 answer