Find the intervals in which the function ๐ given by ๐(๐ฅ) = tan ๐ฅ − 4๐ฅ, ๐ฅ ∈ (0,π/2) is
(a) strictly increasing (b) strictly decreasing
Last updated at Oct. 27, 2020 by Teachoo
Transcript
Question 32 Find the intervals in which the function ๐ given by ๐(๐ฅ) = tan ๐ฅ โ 4๐ฅ, ๐ฅ โ (0,๐/2) is (a) strictly increasing (b) strictly decreasing ๐(๐ฅ) = tan ๐ฅ โ 4๐ฅ Finding ๐^โฒ (๐) ๐^โฒ (๐ฅ)=ใ๐ ๐๐ใ^2 ๐ฅ โ4 Putting ๐^โฒ (๐) = 0 ใ๐ ๐๐ใ^2 ๐ฅ โ4=0 ใ๐ ๐๐ใ^2 ๐ฅ=4 ใ๐ ๐๐ใ^2 ๐ฅ=2^2 ๐๐๐ ๐=ยฑ๐ Thus, ๐=๐ /๐,๐๐ /๐,๐๐ /๐,โฆโฆโฆ Since ๐ฅ โ (0,๐/2) โด ๐= ๐ /๐ Plotting points on Number line Hence, ๐(๐ฅ) is is strictly decreasing in (๐,๐ /๐) & ๐(๐ฅ) is strictly increasing in (๐ /๐,๐ /๐)
CBSE Class 12 Sample Paper for 2021 Boards
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CBSE Class 12 Sample Paper for 2021 Boards
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