Homework SourseA find the critical points of the following function on the
A find the critical points of the following function on the given interval .
B Use a graphing utility to determine whether the critical points correspond to the local maxima, minima, or neither.
C find the absolute maximum and minimum values on the given interval.
f(theta)=3sintheta+6costheta;[-2pi,2pi]
B Use a graphing utility to determine whether the critical points correspond to the local maxima, minima, or neither.
C find the absolute maximum and minimum values on the given interval.
f(theta)=3sintheta+6costheta;[-2pi,2pi]
Solution
f\'(theta)=3 cos(theta)-6 sin(theta) for critical point f\'(theta)=0 tan(theta)=1/2 theta=tan-1(1/2) theta=26.56 206.56 -163.44 -343.44 for maxima and minima we take f\'\'(theta) f\"(theta)=-3cos(theta)-6sin(theta) f\"(theta)=-(3cos(theta)+6sin(theta)) f\"(theta)<0 for 26.56 so 26.56 is maxima point f\"(theta)>0 for 206.59 so it\'s minima point f\"(theta) <0 for 343.44 so it\'s maxima point f\"(theta) >0 for -163.44 so it\'s minima point
