Misc 13 - Chapter 6 Class 12 Application of Derivatives

Transcript

Misc 13 Find the points at which the function f given by f (𝑥) = ﷐﷐𝑥−2﷯﷮4﷯ ﷐﷐𝑥+1﷯﷮3﷯ has (i) local maxima (ii) local minima (iii) point of inflexion f﷐𝑥﷯= ﷐﷐𝑥−2﷯﷮4﷯﷐𝑥+1﷯3 Step 1: Finding f’﷐𝑥﷯ f’﷐𝑥﷯ = ﷐𝑑 ﷐﷐﷐𝑥−2﷯﷮4﷯﷐﷐𝑥+1﷯﷮3﷯﷯﷮𝑑𝑥﷯ = ﷐﷐﷐﷐﷐𝑥−2﷯﷮4﷯﷯﷮′﷯﷐𝑥+1﷯﷮3﷯+﷐﷐﷐﷐𝑥+1﷯﷮3﷯﷯﷮′﷯﷐﷐𝑥−2﷯﷮4﷯ = 4﷐﷐𝑥−2﷯﷮3﷯﷐﷐𝑥+1﷯﷮3﷯+3﷐﷐𝑥+1﷯﷮2﷯﷐﷐𝑥−2﷯﷮4﷯ = ﷐﷐𝑥−2﷯﷮3﷯﷐﷐𝑥+1﷯﷮2﷯﷐4﷐𝑥+1﷯+3﷐𝑥−2﷯﷯ = ﷐﷐𝑥−2﷯﷮3﷯﷐﷐𝑥+1﷯﷮2﷯﷐4𝑥+4𝑥+3𝑥−6﷯ = ﷐﷐𝑥−2﷯﷮3﷯﷐﷐𝑥+1﷯﷮2﷯﷐7𝑥−2﷯ Step 2: Putting f’﷐𝑥﷯=0 ﷐﷐𝑥−2﷯﷮3﷯﷐﷐𝑥+1﷯﷮2﷯﷐7𝑥−2﷯=0 Hence, 𝑥=2 & 𝑥=−1 & 𝑥=﷐2﷮7﷯ = 0.28 Step 3: Thus 𝑥=−1 is a point of inflexion 𝑥=﷐2﷮7﷯ is point of minima & 𝑥=2 is point of maxima