Question

Statement I: The derivative of the function y=$x^2$ at a point exists.
Statement II: The integral of the function at a point where it is defined exists.
A) Statement I is true, Statement II is true; Statement II is a correct explanation of Statement I.
B) Statement I is true, Statement II is true; Statement II is a not correct explanation of Statement I
C) Statement I is true, Statement II is false.
D)Statement I is false, Statement II is true.

Answer 1

Hint: To solve this problem, knowledge about differentiability is required. If a function is polynomial, it is differentiable at every known point. Also, any function is integrable if it exists at that point.

Complete step-by-step answer:
The given function y=$x^2$ is a polynomial function, hence it is differentiable at all points. So, Statement I is correct. Also, y=$x^2$ exists at every point hence it is integrable at all points. Hence options C. and D. can be eliminated.

Now, we can see that both the statements are true. But it is not necessary that if a function exists at a point, it is differentiable as well. So, Statement II cannot be an explanation for Statement I. Hence, the correct option is B. Statement I is true, Statement II is true; Statement II is a not correct explanation of Statement I.

Note: In such types of questions, first try to find the statement which is false. If one of the statements is false, then we can mark the correct option without checking the other statement. If both statements are true, then check if one statement is the explanation of the other.