Question

Question #d2272

Answer 1

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)`