Mathematics doubt
When to put extreme points of the domain in the function to yield it's range .
Like if x is from [-3,4] and f(x)=x^2 then range of this function is from 0 to 16
And when f(x)=[2(2x-3)^2+1] and x is from (-1,1) then on putting these extreme points i.e. -1&1 , we get range (19,51)
So how we will come to know this ??
9 Replies
@Apu
Note for OP
+solved @user1 @user2... to close the thread when your doubt is solved. Mention the users who helped you solve the doubt. This will be added to their stats.On a given interval , say, [a,b], if the function f has an absolute maxima at x=M and an absolute minimum at x=m, then it's range on the interval [a,b] will always be [f(m), f(M)]
If the function is monotonically increasing on [a,b] it's range is [f(a),f(b)] and if it is monotonically decreasing, the range will be [f(b),f(a)]
So is this function monotonically increasing or decreasing ,
f(x)=[2(2x-3)^2+1]
Check using its derivative
f'(x) = 8(2x-3)
Critical point is at x=3/2, so not in [-1,1]. So it's monotonic on the interval you've specified.
Okay..
Understood ..
Thank you ! @Opt
Just do +solved
+ solved @Opt
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