Find inc/dec interval of the following function:
f(x) = x^4-50x^2+4
My work:
f'(x) = 4x^3-100x
4x^3-100x = 0
4x(x^2-25) = 0
4x = 0 ----> x= 0
x^2-25 = 0----> x = 5, x = -5
So, (-5,0,5) are the critical point....
I cannot find the increasing and decreasing intervals, because when I substittue critical points in f(x) to positive or negative, it just give me negative value.
Can you plz help me by giving me the correct answer.
Thx
Yes! there are intervals, they're just implied!
When you find those critical values, you are locating the place where where the tangent line to f(x) will be horizontal, but you have THREE places where it is horizontal. -5, 5, and 0, so, in these intervals, you must determine whether or not f'(x) (the slope of f(x)) is negative or positive. If it's negative, the function is decreasing, if it's positive the function is decreasing.
So, the intervals are
. Choose an arbitrary # in each one of these intervals and evaluate the slope of f(x)!