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Consider the function f(x) = sin(x) in the interval x [π/4, 7π/4]. The number and location(s) of the
local minima of this function are
  • a)
    One, at π/2
  • b)
    One, at 3π/2
  • c)
    Two, at π/2 and 3π/2
  • d)
    Two, at π/4 and 3π/2
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Consider the function f(x) = sin(x) in the interval x [π/4, 7π/...
f '(s) = cosx =0 gives root π/2 and 3π/2 which lie between given domain in question [π/4,7π/4]

f ''(x)= - (sinx) at π/2 it gives -1<0 it means it is local maxima and at 3π/2 it gives 1>0 which is local minima 

and since, at π/2 it is local maxima so, before it, graph is strictly increasing, so π/4 is also local minima

So, there are two local minima π/4 and 3π/2
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Most Upvoted Answer
Consider the function f(x) = sin(x) in the interval x [π/4, 7π/...
Sin x has a maximum value of 1 at ,
π/2 and a minimum value of –1 at


3π/2 and at all angles conterminal with them.
The graph of f (x) = sin x is
 
  In the interval   
, it has one local minimum x= 3π/2
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Consider the function f(x) = sin(x) in the interval x [π/4, 7π/4]. The number and location(s) of thelocal minima of this function area)One, at π/2b)One, at 3π/2c)Two, at π/2 and 3π/2d)Two, at π/4 and 3π/2Correct answer is option 'D'. Can you explain this answer?
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Consider the function f(x) = sin(x) in the interval x [π/4, 7π/4]. The number and location(s) of thelocal minima of this function area)One, at π/2b)One, at 3π/2c)Two, at π/2 and 3π/2d)Two, at π/4 and 3π/2Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about Consider the function f(x) = sin(x) in the interval x [π/4, 7π/4]. The number and location(s) of thelocal minima of this function area)One, at π/2b)One, at 3π/2c)Two, at π/2 and 3π/2d)Two, at π/4 and 3π/2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider the function f(x) = sin(x) in the interval x [π/4, 7π/4]. The number and location(s) of thelocal minima of this function area)One, at π/2b)One, at 3π/2c)Two, at π/2 and 3π/2d)Two, at π/4 and 3π/2Correct answer is option 'D'. Can you explain this answer?.
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