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Last updated at April 19, 2021 by Teachoo

Example 11 Find the intervals in which the function f given by f (π₯)=4π₯3β6π₯2 β72π₯+30 is (a) strictly increasing (b) strictly decreasing. f (π₯)=4π₯3β6π₯2 β72π₯+30 Calculating fβ(x) f (π₯)=4π₯3β6π₯2β72π₯+30 πβ²(π₯)=12π₯2β12π₯ β72π₯ πβ²(π₯) =12(π₯2βπ₯ β 6) πβ²(π₯) =12(π₯2β3π₯+2π₯ β6) πβ²(π₯) = 12(π₯(π₯ β 3) + 2(π₯ β 3)) πβ²(π)=ππ(π+π)(π βπ) Putting fβ(x) = 0 12(π₯+2)(π₯ β3)=0 (π₯+2)(π₯ β3)=0 So, x = β2 and x = 3 Plotting points on number line Hence, f is strictly increasing in (ββ ,βπ) & (π ,β) f is strictly decreasing in (βπ, π)