 # Find the values of a for which the function f (x) = cos x - sin x + ax + b is decreasing.

9 years ago Thanks & Regards
Parvez Ali Sher Mohammad IIT Delhi
9 years ago
f'(x)=-sinx-cox+a
minimum of -sinx-cosx= -sqrt(2)=-1.4

f'(x)>a-1.4
f'(x)>0
a-1.4>=0
a belongs to(1.4, inf)

B.tech, IIT Delhi

9 years ago
Check the monotonicity of f(x) = x sin x in (0; =2)
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Let a = min  x2 + 4x + 5; x 2 R and b = lim!0 1??cos 2 2 then nd the value of a??b a+b . bharat bajaj IIT Delhi
9 years ago
f(x) = cos x - sin x + ax + b
df/dx = -sin x -cos x + a
For function to be decreasing, df/dx<0
Hence, -sinx - cosx +a <0
sinx + cosx>a
or root(2) sin (x+pi/4) > a
sin (x + pi/4) > a/root2
a/root2< -1
a< -root2
Hence, the value of a should be (-inf, root 2) for the function to be decreasing.
Thanks & Regards
Bharat Bajaj bharat bajaj IIT Delhi
`f(x) = cos x - sin x + ax + bdf/dx = -sin x -cos x + aFor function to be decreasing, df/dx<0Hence, -sinx - cosx +a <0sinx + cosx>aor root(2) sin (x+pi/4) > asin (x + pi/4) > a/root2a/root2< -1a< -root2Hence, the value of a should be (-inf, -root 2) for the function to be decreasing.Thanks & RegardsBharat BajajaskIITians FacultyIIT Delhi` Sher Mohammad IIT Delhi
`f'(x)=-sinx-cosx+a <0the minmum value of -sinx-cosx, occurs at pi/4 = -sqrt(2)=-1.41a-1.41<0a<1.41Sher MohammadB.Tech, IIT Delhi`