Ex 6.3

Chapter 6 Class 12 Application of Derivatives
Serial order wise

Transcript

Ex 6.3, 3 Find the local maxima and local minima, if any, of the following functions. Find also the local maximum and the local minimum values, as the case may be: (iii) β(π₯)=sinβ‘π₯+cosβ‘π₯, 0<π₯<π/2 β(π₯)=sinβ‘π₯+cosβ‘π₯, 0<π₯<π/2 Finding πβ²(π) ββ²(π₯)=π(sinβ‘π₯ + cosβ‘π₯" " )/ππ₯ β^β² (π₯)=cosβ‘π₯βsinβ‘π₯ Putting πβ²(π)=π cosβ‘π₯βπ πππ₯=0 cosβ‘γπ₯=π ππ π₯γ 1 = sinβ‘π₯/cosβ‘π₯ 1 = tan π₯ tan π₯=1 β΄ π₯=45Β°= π/4 Finding hββ(π) hβ(π₯)=cosβ‘π₯βsinβ‘π₯ hββ(π₯)=βsinβ‘π₯βcosβ‘π₯ Putting π=π/π hββ(Ο/4)=βsin(Ο/4)βπππ (Ο/4) = β 1/β2β1/β2 = (β2)/β2 = β β2 Since hββ(π₯)<0 when π₯=Ο/4 β΄ π₯=Ο/4 is point of Local Maxima f has Maximum value at π=π/π f(π₯)=π πππ₯+πππ π₯ f(Ο/4)=π ππ(Ο/4)+πππ (Ο/4) = 1/β2+1/β2 = 2/β2 = βπ