find max and min value of function f(x)=7cosx-24sinx+5
Answers
Answered by
1
Answer:
12 & -19
Step-by-step explanation:
f(x) = 7 cos x - 24 sin x + 5
f '(x) = - 7 sin x -24 cos x
for f ' (x) = 0
- 7 sin x -24 cos x = 0
7 sinx = - 24 cos x
for f " (x) = - 7 cos x + 24 sin x
i,e. f " (x) = - 7 cos x + 24 ( - 24/7 cos x )
f " (x) = - 625/7 cos x
for x = 0° f " (x) = - 625/7 < 0 & f is max
for x = 90° f " (x) = 0 & f is max/min
for x = 180° f " (x) = 625/7 > 0 f is min
hence...
f(0°) = 7 cos 0° -24sin 0° + 5= 12 (max)
f(90°)= 7cos 90°-24sin90°+5 = -19 (min)
f(180°) =7cos 180° -24 sin180° +5 = -2(min)
therefore...
f max = 12 & f min = -19
Answered by
11
Now,
_______________________________________________________
HOPE THIS IS HELPFUL...
Similar questions