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What is the minimum angle by which the coordinate axes have to be rotated in anticlockwise sense (in Degrees), such that the function f(x) = 3x3 + 5x + 1016 has at least one Rolles point
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Correct answer is option 'C'. Can you explain this answer?
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What is the minimum angle by which the coordinate axes have to be rota...
For the transformed function to have a Rolles point is equivalent to the existing function having a Lagrange point somewhere in the real number domain, we are finding the point in the domain of the original function where we have f'(x) = tan(α)
Let the angle to be rotated be α
We have
f'(x) = 9x2 + 5 = tan(α)
9x2 = tan(α) – 5
For the given function to have a Lagrange point we must have the right hand side be greater than zero, so
tan(α) – 5 > 0
tan(α) > 5
α > tan-1(5)
In degrees we must have,
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What is the minimum angle by which the coordinate axes have to be rotated in anticlockwise sense (in Degrees), such that the function f(x) = 3x3 + 5x + 1016 has at least one Rolles pointa)b)c)d)Correct answer is option 'C'. Can you explain this answer?
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