Question

The value of b for which the function f(x) = sinx – bx + c is a strictly decreasing function ∀x ϵ R is (a) b ϵ ( -1, 1) (b) b ϵ ( - ∞, 1) (c) b ϵ (1, ∞) (d) b ϵ *1, ∞)​

Answer 1

b∈(1,∞)

A function is strictly decreasing in the range when

dx

d(f(x))

<0

dx

d(f(x))

=

dx

d(sin x−bx+c)

=cos x−b

⇒cos x−b<0 or b>cos x

Since the range of cos x is [−1,1] implies b∈(1,∞)

Step-by-step explanation:

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