Question #d2272

1 Answer
Narad T.
Nov 9, 2017

The interval is #=(-0.875,-0.8671875)#

Explanation:

The Intermediate Value Theorem States that :

If #f(x)# is a continuos function on the interval #[a,b]# and #N# is any number between #f(a)# and #f(b)# where #f(a)!=f(b)#, then there exists a number #c# in the interval #(a,b)# such that #f(c)=N#

Here,

#f(x)=x^5-x^2+2x+3#

#f(0)=0-0+0+3=3#

#f(-1)=(-1)^5-(-1)^2+2(-1)+3=-1#

#EE c in (-1,0)# such that #f(c)=0#

#f(-0.5)=1.71875#

So, #c in (-1,-0.5)#

#f(-0.75)=0.7#

#c in (-1,-0.75)#

#f(-0.875)=-0.0285#

#c in (-0.875,-0.75)#

#f(-0.8125)=0.361#

#c in (-0.875,-0.8125)#

#f(-0.84375)=0.173#

#c in (-0.875,-0.84375)#

#f(-0.859375)=0.074

Therefore,

#x in (-0.875,-0.859375)#

#f(-0.8671875)=0.023#

So,

#c in(-0.875,-0.8671875)#

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