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For the function f(x) x^4-8x^2+10 determine the value(s) of x for which f(x) is monotonic increasing?
and monotonic decreasing. Could someone also explain what this means? Thanks
So would increasing be x>2 and x>-2?
1 Answer
- 8 years agoFavorite Answer
monotonic decreasing means for given values of x the value ofthe functions will increase. This can be found by differentiation method. Differentiate the function f(x) with respect to x. Then using inequality U can find the required interval. For monotonic increasing the f'(x) will be greater than zero and for monotonic decreasing the value of f'(x) will be less than zero. For given problem.
F(x)= x^4-8x^2+10
F'(x)=d/dx(x^4-8x^2+10)
. =4x^3-16x
As we need to find in which interval it is strictly decreasind
Putting 4x^3-16x<0
4x^3<16x
x^3<4x
x^2<4
-2<x<2
x belongs to (-2,2)
Source(s): I m a geek :-D