1q1.
sin3x-[-1,1]
so range of the given fn is-[1/3,1]
Q4.Differentiate,
so cosx-b<0,as the fn is decreasing.
3.-6
psoting some doubts of functions here...plzz help...
1. range of f(x) = 12-sin 3x, m getting [1/2,1]...but the answer is [1/3,1].
2. If f(x) is an odd peridic function with period 2 then f(4) equals...??
3. f:R→R...then f(x) = x^3 + x^2 f'(1) + xf"(2) + f"'(3) then f(2) - f(1)...???
4. the value of b for which the function f(x) = sin x - bx + c is decreasing in the interval (-infinit, infinity) is?
Can i use the first derivative metho in the fourth q???
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8 Answers
1
23Q3)
let,f′(1)=a,f′′(2)=b,f′′′(3)=c
f(x)=x3+ax2+bx+c
also , from 2 , and from 1 ,
.........(4)
f′(1)=a=3+2a+b
......(5)
from 4,5
b=2, a= - 5
so
f(x)=x3−5x2+2x+6
f(2)-f(1) = (8 - 20 + 10 ) - ( 1 - 5 + 2 + 6 )
=−6
23Q2 ->
not sure but there are 2 methods ,
also,f(x)=f(x+2).......(1)
so,f(4)+f(−4)=0
f(4)+f(−4+2)=0......(from1)
f(4)+f(−4+2+2)=0......(from1)
f(4)+f(−4+2+2+2)=0......(from1)
f(4)+f(−4+2+2+2+2)=0......(from1)
OR,
since no other specific condition is attached to the function , we can take it as any standard odd function with period = 2
eg:f(x)=sin(πx)
is an odd function wid period 2 , defined for all x ,
and clearly f(4) = 0
23f(x) = sinx - bx+ c
f'(x) = cosx - b
for function to be always decreasing
f'(x) < 0
this cosx < b
thus b must be gr8er than the gr8est value of cosx
hence b > 1