The function f is such thatfx)a-bcosx for 0<x<360, where a and b are positive constants .the maximum value of fx is 10 and minimum is-2 find a and b?

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Answer 1 · 2017-11-14T21:41:47

#color(blue)(a=4)#

#color(blue)(b=6)#

Note:

You have to include #0# in the interval, because this is where the minimum value of #-2# occurs. So interval should be:

#0<=x<360^o#

#f(x)=a-bcosx#

For interval #0 <= x < 360^o#, the greatest value of #cosx=1#. This occurs when #x=0^o# the minimum value of #cosx= -1# this occurs when #x=180^o#

So maximum value:

#a-bcos(180)= 10#

#a-b(-1)=10#

#a+b=10##color(white)(88)[1]#

Minimum value:

#a-bcos(0)=-2#

#a-b(1)=-2#

#a-b=-2##color(white)(88)[2]#

Solve #[1] and [2]# simultaneously:

Subtract [2] from [1]:

#a+b=10#
#a-b=-2#

#2b=12=>b=6#

using [2]:

#a-6=-2=>a=4#

#:.#

#color(blue)(a=4)#

#color(blue)(b=6)#