This statement is true or false?Please give reasons for your answer. Rolle's Theorem is applicable for the function f,defined by f(x)=1+x^(2/3) in the interval [-1,1] ?
1 Answer
Please see below.
Explanation:
When we are asked whether some theorem "can be applied" to some situation, we are really being asked "Are the hypotheses of the theorem true for this situation?"
(The hypotheses are also called the antecedent, of 'the if parts'.)
So we need to determine whether the hypotheses ot Rolle's Theorem are true for the function
Rolle's Theorem has three hypotheses:
H1 :
H2 :
H3 :
We say that we can apply Rolle's Theorem if all 3 hypotheses are true.
H1 : The function
H2 : The function
H3 :
If even one hypothesis fails to be true, then we cannot apply the theorem.
Therefore we CANNOT apply Rolle's Theorem to
By the way, the conclusion of Rolle's Theorem is also false for this function on this interval. There is no solution to