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Check monotonocity of f(x)=x^3+ 2x^2 +5x for x 3sinx for x>0 at x=0

Check monotonocity of
f(x)=x^3+ 2x^2 +5x for x
        3sinx for x>0
   at x=0

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
9 years ago
Ans:
Hello student,
Please find the answer to your question below

f(x) = x^3 + 2x^2 + 5x; x < 0
f'(x) = 3x^2 + 4x + 5
f'(x) > 0
> f(x) is always increasing below zero.
f(x) = 3sinx; x > 0
f'(x) = 3cosx
f’(x) is +ve in the positive nbhd of zero. So its increases in the +ve nbhd of zero.
f(x) is monotonic at a point.



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