Let be a twice differentiable function defined on such that , and for all . If , for all , then the value of lies in the interval:
Explanation for correct option(s)
Option B:
Given data
for all
Consider the given equation as,
Divide by in Equation (1)
Rewrite the above Equation as,
Integrating both side
Integrating the above Equation with respect to .
We know that
Then the Equation (2) becomes
If , from the given data
From the given data
If ,
The Approximate value of
Since, the value of is lies between the interval
Hence, the correct answer is Option B.