The interval in which the function f(x)=3x3+x2−7x+13 is decreasing is
A
(−1,19)
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B
(−1,98)
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C
(−1,89)
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D
(−1,79)
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Solution
The correct option is D(−1,79) f(x)=3x3+x2−7x+13 f′(x)=9x2+2x−7⇒f′(x)=9x2+9x−7x−7⇒f′(x)=(x+1)(9x−7) For the given function to be decreasing in nature f′(x)<0⇒(x+1)(9x−7)<0⇒x∈(−1,79)