Ex 6.2, 5 - Chapter 6 Class 12 Application of Derivatives
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 6.2, 5 Find the intervals in which the function f given by f (๐ฅ) = 2๐ฅ3 โ 3๐ฅ2 โ 36๐ฅ + 7 is (a) strictly increasing (b) strictly decreasingf(๐ฅ) = 2๐ฅ3 โ 3๐ฅ2 โ 36๐ฅ + 7 Calculating fโ(๐) fโ(๐ฅ) = 6๐ฅ2 โ 6๐ฅ โ 36 + 0 fโ(๐ฅ) = 6 (๐ฅ2 โ ๐ฅ โ 6 ) fโ(๐ฅ) = 6(๐ฅ^2 โ 3๐ฅ + 2๐ฅ โ 6) fโ(๐ฅ) = 6(๐ฅ(๐ฅ โ 3) + 2 (๐ฅ โ 3)) fโ(๐) = 6(๐ โ 3) (๐ + 2) Putting fโ(x) = 0 6(๐ฅ+2)(๐ฅ โ3)=0 (๐ฅ+2)(๐ฅ โ3)=0 So, x = โ2 and x = 3 Plotting points on number line Hence, f is strictly increasing in (โโ ,โ๐) & (๐ ,โ) f is strictly decreasing in (โ๐, ๐)
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