Question

Give the procedure to find the interval for which Rolle's theorem is vaalid for the function f[x]=2x^3+x^2-4x

+2

Answer 1

Is it \(f(x)=2x^3+x^2-4x\) or \(f(x)=2x^3+x^2-4x + 2\)?

Answer 2

Either way, you should be looking for the real roots of the function.

Answer 3

Find a pair of roots or \((x, y)\) such that \(f(x)=0\), \(f(y)= 0\) and \(x \neq y\). Since the function is continuous and differentiable everywhere, it will be continuous on \([x, y]\) and differentiable on \((x, y)\). All this together satisfies the requirements for Rolle's theorem.

Answer 4

I should mention that you can find zeros of a function numerically using Newton's method.

Answer 5

we obtain fractional roots. we might have integral ans when the condition is like f(a)=f(b) = non zero..if such integral a and b exist then we should prefer this one....

Answer 6

Do you mean integer answer?

Answer 7

It really doesn't matter if the roots are at integer points or not.

Answer 8

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