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Find the intervals in which f(x)=4x^(3)-...

Find the intervals in which `f(x)=4x^(3)-45x^(2)+168x-16` is (i) Strictly increasing (ii) Strictly decreasing

Text Solution

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`f(x)=4x^(3)-45x^(2)+168x-16` ltbr? `f'(x)=12x^(2)-90x+168`
`= 6(2x^(2)-15x+28)`
`f'(x)=6(x-4)(2x-7)`
(i) For strictly increasing
`f'(x) gt 0`
`implies (x-4)(2x-7) gt 0`
`implies x in (-oo,(7)/(2)) cup (4,oo)`

(ii) For strictly decreasing
`f'(x) lt 0`
`implies (x-4)(2x-7) lt 0`
`implies x in ((7)/(2),4)`
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