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