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Consider the following statements:
1. f(x) = In x is an increasing function on (0, ∞).
2. f(x) = ex - x (In x) is an increasing function on (1, ∞).
1. f(x) = In x is an increasing function on (0, ∞).
2. f(x) = ex - x (In x) is an increasing function on (1, ∞).
Q. Which of the above statements is/are correct ?
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor2
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the following statements:1. f(x) = In x is an increasing func...
f(x) = logx
Clearly f(x) is increasing on (0,∞)
f(x) = ex-xlogx
f '(x) = ex - (log x +1)
Clearly f(x) is increasing on (0,∞)
f(x) = ex-xlogx
f '(x) = ex - (log x +1)
From the figure it is clear that f'(x) > 0 on (1, ∞).
So both statements (1) & (2) are correct.
So both statements (1) & (2) are correct.
Most Upvoted Answer
Consider the following statements:1. f(x) = In x is an increasing func...
∞)
2. f(x) = x^2 is a decreasing function on (-∞, 0)
Which of the statements is true?
1. The first statement is true. The natural logarithm function, ln(x), is increasing on the interval (0, ∞). This means that as x increases, the value of ln(x) also increases.
2. The second statement is false. The function f(x) = x^2 is actually an increasing function on the interval (-∞, 0). As x decreases, the value of x^2 also decreases. Therefore, the function is not decreasing on this interval.
2. f(x) = x^2 is a decreasing function on (-∞, 0)
Which of the statements is true?
1. The first statement is true. The natural logarithm function, ln(x), is increasing on the interval (0, ∞). This means that as x increases, the value of ln(x) also increases.
2. The second statement is false. The function f(x) = x^2 is actually an increasing function on the interval (-∞, 0). As x decreases, the value of x^2 also decreases. Therefore, the function is not decreasing on this interval.
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Consider the following statements:1. f(x) = In x is an increasing function on (0, ∞).2. f(x) = ex - x (In x) is an increasing function on (1, ∞).Q. Which of the above statements is/are correct ?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor2Correct answer is option 'C'. Can you explain this answer?
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