The value of ' a ' for which the function f(x)= sin x- cos x-a x+b decreases for all real values of x, is -

Question

The value of ' a ' for which the function f(x)= sin x- cos x-a x+b decreases for all real values of x, is - (A) a ≥-√2 (B) a ≤-√2 (C) a ≤ √2 (D) a ≥ √2

Tardigrade Admin · Accepted Answer

f ( x )= sin x - cos x - ax + b f prime( x )= cos x + sin x - a ≤ 0 ∀ x ∈ R ⇒ a ≥ cos x + sin x ∀ x ∈ R ⇒ a ≥ √2

Q. The value of ' $a$ ' for which the function $f (x) = sin x - cos x - a x + b$ decreases for all real values of $x$ , is -

$a \geq - 2$

$a \leq - 2$

$a \leq 2$

$a \geq 2$

$f (x) = sin x - cos x - a x + b$
$f^{'} (x) = cos x + sin x - a \leq 0\forall x \in R$
$\Rightarrow a \geq cos x + sin x \forall x \in R$
$\Rightarrow a \geq 2$

Q. The value of ' a ' for which the function f(x)=sinx−cosx−ax+b decreases for all real values of x, is -

a≥−2​

a≤−2​

a≤2​

a≥2​