1. Chapter 6 Class 12 Application of Derivatives
2. Serial order wise
3. Ex 6.2

Transcript

Ex 6.2,8 Find the values of ð¥ for which y = [ð¥(ð¥ â 2)]2 is an increasing function ð¦ =ï·ï·ð¥ï·ð¥â2ï·¯ï·¯ï·®2ï·¯ Step 1: Finding ï·ðð¦ï·®ðð¥ï·¯ ð¦ =ï·ï·ð¥ï·ð¥â2ï·¯ï·¯ï·®2ï·¯ ð¦ =ï·ï·ï·ð¥ï·®2ï·¯â2ð¥ï·¯ï·®2ï·¯ ð¦ =ï·ï·ð¥ï·¯ï·®4ï·¯+ï·ï·2ð¥ï·¯ï·®2ï·¯â2ï·ï·ð¥ï·®2ï·¯ï·¯ï·2ð¥ï·¯ ð¦ = ï·ð¥ï·®4ï·¯+4ï·ð¥ï·®2ï·¯â4ï·ð¥ï·®3ï·¯ Diff. w.r.t ð¥ ï·ðð¦ï·®ðð¥ï·¯=ï·ðï·ï·ð¥ï·®4ï·¯+4ï·ð¥ï·®2ï·¯â4ï·ð¥ï·®3ï·¯ï·¯ï·®ðð¥ï·¯ ï·ðð¦ï·®ðð¥ï·¯=4ï·ð¥ï·®3ï·¯+8ð¥â12ï·ð¥ï·®2ï·¯ ï·ðð¦ï·®ðð¥ï·¯=4ð¥ï·ï·ð¥ï·®2ï·¯+2â3ð¥ï·¯ ï·ðð¦ï·®ðð¥ï·¯=4ð¥ï·ï·ð¥ï·®2ï·¯â3ð¥+2ï·¯ ï·ðð¦ï·®ðð¥ï·¯=4ð¥ï·ï·ð¥ï·®2ï·¯â2ð¥âð¥+2ï·¯ ï·ðð¦ï·®ðð¥ï·¯=4ð¥ï·ð¥ï·ð¥â2ï·¯â1ï·ð¥â2ï·¯ï·¯ ï·ðð¦ï·®ðð¥ï·¯=4ð¥ï·ï·ð¥â1ï·¯ï·ð¥â2ï·¯ï·¯ ï·ðð¦ï·®ðð¥ï·¯=4ð¥ï·ð¥â1ï·¯ï·ð¥â2ï·¯ Step 2: Putting ï·ðð¦ï·®ðð¥ï·¯=0 4ð¥ï·ð¥â1ï·¯ï·ð¥â2ï·¯=0 So, ð¥=0 , ð¥=1 & ð¥=2 Step 3: Plotting points on real line The points ð¥ = 0 , 1 and 2 divide the real line into 4 disjoint intervals i.e. ï·âð´0ï·¯ , ï·0 , 1ï·¯ , ï·1 , 2ï·¯ & ï·2 ,ð´uc1ï·¯ Step 4: Thus the function y = ï·ð¥ï·ï·ð¥â1ï·¯ï·®2ï·¯ï·¯ is strictly increasing for 0 <ð¥<1 and ð¥>2 Thus the function y = ï·ð¥ï·ï·ð¥â1ï·¯ï·®2ï·¯ï·¯ is strictly increasing for 0 <ð<ð and ð>ð

Ex 6.2