+0

# intermediate value

0
551
6
+1832

I think therr is a mistake here, they put fx is equal to ' 0 '   !

xvxvxv  Oct 10, 2014

### Best Answer

#1
+92674
+10

The Intermediate Value Theorem says that , in some interval [a, b], if f(a) and f(b) have opposite signs, then f(x) has at least one "root" in this interval. (As long as f(x) is continuous on the interval !!)

So

f(0) = (0)^3 + 4(0) - 4 = -4

and

f(1) = (1)^3 + 4(1) - 4 =  1

Then, at x=0 the function lies below the x axis, and at x =1, the function lies above the x axis........and since polynomials are always continuous, this function must cross the x axis on [0,1]

So...this tells us that this ploynomial has at least one"zero" (root) on the interval [0, 1]....In other words, whatever this value is, it makes f(x) = 0......(the "0" in the problem is correct !!!......)

CPhill  Oct 10, 2014
#1
+92674
+10
Best Answer

The Intermediate Value Theorem says that , in some interval [a, b], if f(a) and f(b) have opposite signs, then f(x) has at least one "root" in this interval. (As long as f(x) is continuous on the interval !!)

So

f(0) = (0)^3 + 4(0) - 4 = -4

and

f(1) = (1)^3 + 4(1) - 4 =  1

Then, at x=0 the function lies below the x axis, and at x =1, the function lies above the x axis........and since polynomials are always continuous, this function must cross the x axis on [0,1]

So...this tells us that this ploynomial has at least one"zero" (root) on the interval [0, 1]....In other words, whatever this value is, it makes f(x) = 0......(the "0" in the problem is correct !!!......)

CPhill  Oct 10, 2014
#2
+1832
0

Thank you Cphill ..

but I think that this sentence Suffice

" has at least one solution ''

xvxvxv  Oct 10, 2014
#3
+1832
0

right ?

xvxvxv  Oct 12, 2014
#4
+94105
0

You want to add in the given domain [0,1] because that is what the question asked for.

Melody  Oct 12, 2014
#5
+1832
0

So is my answer correct?

xvxvxv  Oct 12, 2014
#6
+94105
0

Yes looks good.

Personally I would say Hence rather than yes but it shouldn't really matter.

Also, you answer is correct but the original question gave the interval  [0,1]

so personally I would have repeated exactly what they asked for but again it is trivial.

Melody  Oct 12, 2014

### New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.