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If f(x) = x3 - 4x + p, and f(0) and f(1) are of opposite sign, then which of the following is necessarily true ?
- a)-1 < p < 2
- b)0 < p < 3
- c)-2 < p < 1
- d)-3 < p < 0
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If f(x) = x3- 4x + p, and f(0) and f(1) are of opposite sign, then whi...
f(0) = p
f (1) = 1 – 4 + p = p + 3.
p and p+3 are of different signs.
Substitute for the options:
1st option, if p is a negative number, then p – 3 is also negative, and both are same sign.
For 3rd and 4th option, also it is the same.
For the 2nd option, value of p is between 0 and 3, and p – 3 is negative. Hence it agrees.
Even without substituting the answer can be found out. As p and p – 3 are different signs; p should be between 0 and 3.
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
If f(x) = x3- 4x + p, and f(0) and f(1) are of opposite sign, then whi...
The statement "f(0) and f(1) are of opposite sign" means that f(0) < 0="" and="" f(1)="" /> 0, or f(0) > 0 and f(1) < />
We can substitute x = 0 and x = 1 into the function to determine the sign of f(0) and f(1):
f(0) = (0^3) - 4(0) = 0
f(1) = (1^3) - 4(1) = -3
Since f(0) = 0 and f(1) = -3, f(0) and f(1) are of opposite sign.
Therefore, the statement "-1" is necessarily true.
We can substitute x = 0 and x = 1 into the function to determine the sign of f(0) and f(1):
f(0) = (0^3) - 4(0) = 0
f(1) = (1^3) - 4(1) = -3
Since f(0) = 0 and f(1) = -3, f(0) and f(1) are of opposite sign.
Therefore, the statement "-1" is necessarily true.
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If f(x) = x3- 4x + p, and f(0) and f(1) are of opposite sign, then which of the following is necessarily true ?a)-1 < p < 2b)0 < p < 3c)-2 < p < 1d)-3 < p < 0Correct answer is option 'B'. Can you explain this answer?
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