Applications Of Derivatives Question 277

Question: The function $ f(x)=2x^{3}-3x^{2}+90x+174 $ is increasing in the interval

[J & K 2005]

Options:

A) $ \frac{1}{2}<x<1 $

B) $ \frac{1}{2}<x<2 $

C) $ 3<x<\frac{59}{4} $

D) $ -\infty <x<\infty $

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Answer:

Correct Answer: D

Solution:

$ {f}’,(x)=6,(x^{2}-x+15)>0,\forall ,x $ .