practice application task

[sisqo1111]

hi all
my teacher gave us a few prac questions before our sac next week. now whilst she was teaching all of this stuff i didnt really pay attention lol, cause i was studying for midyears.
this is one of the questions if someone could help me out

find the gradient function of: y=18 cos(pi x/80)+12, 0<x<180

and then state the coordinates when the magnitude is at its maximum

thankyou for any help

[Mao]

gradient function is simply the derivative:



assuming that you want to find the magnitude of the gradient is at its maximum, this implies that the gradient function is at its maximum.

this means that the term will be at its maximum,





then just gotta sub this back into y to find out the y coordinate.

[sisqo1111]

thanks a heap Mao
your a gun
ill sure be posting if i need any other help! methods is becoming my worst subject

[sisqo1111]

gradient function is simply the derivative:



just one question, how exactly did you find the grad so quick? were there any other steps involved?

[Mao]

simple differentiation via chain rule:



which simplifies to the above
I cut steps

ps: i made a mistake, there's no +12 at the end...

[sisqo1111]

thankyou