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Question

Consider the function f(x)=0.75x4−x3−9x2+7.
Consider the following statements:
1. The function attains local minima at x=−2 and x=3.
2. The function increases in the interval (−2,0).
Which of the above statements is/are correct?

A
1 only
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B
2 only
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C
Both 1 and 2
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D
Neither 1 nor 2
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Solution

The correct option is C Both 1 and 2
f(x)=0.75x4x39x2+7
Now, df(x)dx=0
3x33x218x=0
x=0,2,3
f′′(x)=9x26x18f′′(0)=18<0f′′(2)=30>0f′′(3)=45>0
Thus, the function attains local minima at x=2 and x=3
Also, from the figure the function increases in the interval (2,0)
Hence, both the statements are correct.

679901_629986_ans_180a3c6cb0484f4797a13ed720c3aabc.png

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