How do you use the Intermediate Value Theorem to show that the polynomial function #f(x)=17x^4-7x^2+9x-1# in the interval #[-2,0]#?

1 Answer
Narad T.
Sep 3, 2017

See the explanation below

Explanation:

The Intermediate Value Theorem states that if #f(x)# is a continuous function on the interval #[a,b]# and #N in (f(a), f(b)) #, then there exists #c in [a,b]# such that #f(c)=N#

Here,

#f(x)=17x^4-7x^2+9x-1# is continuous on #RR# as it is a polynomial function.

The interval is #I= [-2,0]#

#f(-2)=225#

#f(0)=-1#

#f(x) in [225, -1]#

Then,

#f(x)=0# when #x=-1#

#f(-1)=0#

#f(0) in [225, -1]# and #-1 in [-2,0]#

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