maths

Question

Q.9
(B) 4
(C) 7
(D) 8
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

Answer 1

if u r aware with sin(x) graph then u can directly say answer is b

now see rational proof:

f(x)=sinx , f'(x)=cos(x) , f"(x)=-sin(x)

put f'(x)=0

cos(x)=0

therefore x=n(pi)+pi/2, hence f"(x)=-sin(n*pi+pi/2)= -cos(n*pi)

therefore for all odd values of n, f"(x) will be positive hence local minima will occur here

now in given question if x=3pi/2 i.e  x= pi+pi/2 therefore n= 1 (odd) option b is correct