Find the values of b for which the function f(x) = sin x – bx + c is

1.	Find the values of b for which the function f(x) = sin x – bx + c is a decreasing function on R ?
Answer» We have, f(x) = sin x – bx + c f'(x) = cos x - b Given that f(x) is on decreasing function on R \(\therefore\) f'(x) < 0 for all x ∈ R \(\Rightarrow\) cos x - b > 0 for all x ∈ R \(\Rightarrow\) b < cos x for all x ∈ R But the last value of cos x in 1 \(\therefore\) b ≥ 1

Find the values of b for which the function f(x) = sin x – bx + c is a decreasing function on R ?

Answer»

We have,

f(x) = sin x – bx + c

f'(x) = cos x - b

Given that f(x) is on decreasing function on R

\(\therefore\) f'(x) < 0 for all x ∈ R

\(\Rightarrow\) cos x - b > 0 for all x ∈ R

\(\Rightarrow\) b < cos x for all x ∈ R

But the last value of cos x in 1

\(\therefore\) b ≥ 1