# 11.6 Directional Derivatives - 2.pdf - Recall Directional...

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Recall Directional derivative DAN yo Gate of change et f at Goyo into it where it a unit vector Dif No Yok Of No yo it where Of No yo fy Go yo fy No yo gradient vector Maximizing directional deviate directional derivative in of fay at P rate of change off in T direction at P Q M what direction f changes fastest What is the maximum value of the rate A Change If f differentiable then the maximum of the directional derivative is He It happens when it Is the same direction of Any
Example tablet Find the retreat f at pao directional derivative Def ao into ti where Q In what direction does f have the maximum rate of changes What is the maximum value of A et yet of Go 1 E ࠁܻ Go E ܳ 2 I E ܳ at it ׮ܴ DAC ܻ੉ ftp.o G 2 ՘ ޤ׮ maximum value happens When it is parallel to of Go Of Go 10Ha ޷ 1 ݜ maximum rate of change 17 ੄ઁ 1 1 ݒ E
Example TG.gr 1tx g 2 te temperature at unnerve Nc YR In which direction does the temperature increases fastest at 1.1.2 what Is the maximum rate of change 2 80 3208 4802ns 5BIT 0T x g 3ER at 1.1 ߬ୌ g ۄઁ 2 X 2g 32 IT ii 2 1 Alt ۄ޷য় 3 6 160T ੿ ز 1.2 6 be ߓ 1 ز G2 tn lF
Tangent Plane to level surfaces a surface with Fayez k a level surface for F