DSSSB TGT/PGT/PRT Exam > DSSSB TGT/PGT/PRT Questions > Which one of the following is correct in resp...
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Which one of the following is correct in respect of the function f (x)=|x|+x2 ?
- a)f(x) is not continuous at x=0.
- b)f(x)is differentiable at x=0.
- c)f(x)is continuous but not differentiable at x=0.
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Which one of the following is correct in respect of the function f (x)...
Given function f(x) =|x|+x2
again defining the function f(x)
also f(0) = 0
∴ LHL = RHL = f(0) = 0
So function is continuous at x = 0
So f(x) is not differentiable at x = 0.
again defining the function f(x)
also f(0) = 0
∴ LHL = RHL = f(0) = 0
So function is continuous at x = 0
So f(x) is not differentiable at x = 0.
Most Upvoted Answer
Which one of the following is correct in respect of the function f (x)...
Explanation:
Function f(x)=|x|+x^2:
- The given function f(x)=|x|+x^2 consists of two parts:
1. |x| which represents the absolute value of x.
2. x^2 which is the square of x.
Continuity at x=0:
- In order to determine the continuity of the function at x=0, we need to check if the left-hand limit, right-hand limit, and the value at x=0 are equal.
- For f(x)=|x|+x^2, the function is continuous at x=0 as the left-hand limit, right-hand limit, and the value at x=0 are all equal.
Differentiability at x=0:
- To determine the differentiability of the function at x=0, we need to check if the derivative exists at x=0.
- The function f(x)=|x|+x^2 is not differentiable at x=0 because the function is not smooth at this point due to the absolute value function.
Conclusion:
- Therefore, the correct statement is that f(x) is continuous but not differentiable at x=0, which is option 'C'. This is because the function is continuous at x=0 but not differentiable at that point due to the presence of the absolute value function.
Function f(x)=|x|+x^2:
- The given function f(x)=|x|+x^2 consists of two parts:
1. |x| which represents the absolute value of x.
2. x^2 which is the square of x.
Continuity at x=0:
- In order to determine the continuity of the function at x=0, we need to check if the left-hand limit, right-hand limit, and the value at x=0 are equal.
- For f(x)=|x|+x^2, the function is continuous at x=0 as the left-hand limit, right-hand limit, and the value at x=0 are all equal.
Differentiability at x=0:
- To determine the differentiability of the function at x=0, we need to check if the derivative exists at x=0.
- The function f(x)=|x|+x^2 is not differentiable at x=0 because the function is not smooth at this point due to the absolute value function.
Conclusion:
- Therefore, the correct statement is that f(x) is continuous but not differentiable at x=0, which is option 'C'. This is because the function is continuous at x=0 but not differentiable at that point due to the presence of the absolute value function.
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Which one of the following is correct in respect of the function f (x)=|x|+x2?a)f(x) is not continuous at x=0.b)f(x)is differentiable at x=0.c)f(x)is continuous but not differentiable at x=0.d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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