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Suppose the function f(x) = xn , n ≠ 0 is differentiable for all x. Then n can be any element of the interval
- a)[1, ∞]
- b)(0, ∞)
- c)(1/2, ∞)
- d)None of the above
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Suppose the function f(x) = xn, n≠ 0 is differentiable for all x. T...
f(x) = xn , n ≠ 0.
⟹ f ′ (x) = nxn-1
f(x) to be differentiable, n − 1 ≥ 0
f(x) to be differentiable, n − 1 ≥ 0
⟹ n ≥ 1 ⟹ n ∈ [1, ∞]
Most Upvoted Answer
Suppose the function f(x) = xn, n≠ 0 is differentiable for all x. T...
In the given function f(x) = xn, n is the exponent. The exponent determines the power to which x is raised. Let's analyze a few cases based on the value of n:
1. n = 0:
When n is 0, the function becomes f(x) = x^0. Any number raised to the power of 0 is equal to 1. So, f(x) = 1 for all x.
2. n = 1:
When n is 1, the function becomes f(x) = x^1. Any number raised to the power of 1 is equal to itself. So, f(x) = x.
3. n > 0 (positive):
When n is a positive number, the function represents exponential growth. As x increases, the value of f(x) increases at an increasing rate. The rate of increase depends on the value of n. For example, if n = 2, then f(x) = x^2 represents quadratic growth.
4. n < 0="" />
When n is a negative number, the function represents exponential decay. As x increases, the value of f(x) decreases at a decreasing rate. The rate of decrease depends on the value of n. For example, if n = -1, then f(x) = x^(-1) represents exponential decay.
Note: The behavior of the function f(x) = xn may vary depending on the domain and range of x and the specific value of n.
1. n = 0:
When n is 0, the function becomes f(x) = x^0. Any number raised to the power of 0 is equal to 1. So, f(x) = 1 for all x.
2. n = 1:
When n is 1, the function becomes f(x) = x^1. Any number raised to the power of 1 is equal to itself. So, f(x) = x.
3. n > 0 (positive):
When n is a positive number, the function represents exponential growth. As x increases, the value of f(x) increases at an increasing rate. The rate of increase depends on the value of n. For example, if n = 2, then f(x) = x^2 represents quadratic growth.
4. n < 0="" />
When n is a negative number, the function represents exponential decay. As x increases, the value of f(x) decreases at a decreasing rate. The rate of decrease depends on the value of n. For example, if n = -1, then f(x) = x^(-1) represents exponential decay.
Note: The behavior of the function f(x) = xn may vary depending on the domain and range of x and the specific value of n.
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Suppose the function f(x) = xn, n≠ 0 is differentiable for all x. Then ncan be any element of the intervala)[1, ∞]b)(0, ∞)c)(1/2, ∞)d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?
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Suppose the function f(x) = xn, n≠ 0 is differentiable for all x. Then ncan be any element of the intervala)[1, ∞]b)(0, ∞)c)(1/2, ∞)d)None of the aboveCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Suppose the function f(x) = xn, n≠ 0 is differentiable for all x. Then ncan be any element of the intervala)[1, ∞]b)(0, ∞)c)(1/2, ∞)d)None of the aboveCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Suppose the function f(x) = xn, n≠ 0 is differentiable for all x. Then ncan be any element of the intervala)[1, ∞]b)(0, ∞)c)(1/2, ∞)d)None of the aboveCorrect answer is option 'A'. Can you explain this answer?.
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