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What is the maximum and minimum value of sin x +cos x?
- a)0
- b)1
- c)-1
- d)–√2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
What is the maximum and minimum value of sin x +cos x?a)0b)1c)-1d)&nda...
Let y= sin x + cos x
dy/dx=cos x- sin x
For maximum or minimum dy/dx=0
Setting cosx- sin x=0
We get cos x = sin x
x= π/4, 5π/4
Whether these correspond to maximum or minimum, can be found from the sign of second derivative.
d^2y/dx^2=-sin x - cos x=-1/√2–1/√2 (for x=π/4) which is negative. Hence x=π/4 corresponds to maximum.For x=5π/4
d^2y/dx^2=-(-1/√2)-(-1/√2)=2/√2 a positive quantity. Hence 5π/4 corresponds to minimum
Maximum value of the function
y= sin π/4 + cos π/4= 2/√2=√2
Minimum value is
Sin(5π/4)+cos (5π/4)=-2/√2=-√2
dy/dx=cos x- sin x
For maximum or minimum dy/dx=0
Setting cosx- sin x=0
We get cos x = sin x
x= π/4, 5π/4
Whether these correspond to maximum or minimum, can be found from the sign of second derivative.
d^2y/dx^2=-sin x - cos x=-1/√2–1/√2 (for x=π/4) which is negative. Hence x=π/4 corresponds to maximum.For x=5π/4
d^2y/dx^2=-(-1/√2)-(-1/√2)=2/√2 a positive quantity. Hence 5π/4 corresponds to minimum
Maximum value of the function
y= sin π/4 + cos π/4= 2/√2=√2
Minimum value is
Sin(5π/4)+cos (5π/4)=-2/√2=-√2
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What is the maximum and minimum value of sin x +cos x?a)0b)1c)-1d)–√2Correct answer is option 'D'. Can you explain this answer?
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What is the maximum and minimum value of sin x +cos x?a)0b)1c)-1d)–√2Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about What is the maximum and minimum value of sin x +cos x?a)0b)1c)-1d)–√2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the maximum and minimum value of sin x +cos x?a)0b)1c)-1d)–√2Correct answer is option 'D'. Can you explain this answer?.
What is the maximum and minimum value of sin x +cos x?a)0b)1c)-1d)–√2Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about What is the maximum and minimum value of sin x +cos x?a)0b)1c)-1d)–√2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the maximum and minimum value of sin x +cos x?a)0b)1c)-1d)–√2Correct answer is option 'D'. Can you explain this answer?.
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