The set of values of the parameter for which the function; increases and has no critical points is

Question

The set of values of the parameter $' a'$ for which the function; $f (x) = 8 a x - a \sin 6 x - 7 x - \sin 5 x$ increases $\forall x \in R$ and has no critical points is

Smart Achievers · Accepted Answer

(4)

$f (x) = 8 a x - a \sin 6 x - 7 x - \sin 5 x$

$f' (x) = 8 a - 6 a \cos 6 x - 7 - 5 \cos 5 x = 8 a - 7 - 6 a \cos 6 x - 5 \cos 5 x$

$f (x) is an increasing function$

$f' (x) > 0$

$∴$ $8 a - 7 > 6 a + 5 (no critical points)$

$\Rightarrow 2 a > 12$

$\Rightarrow a > 6$

$∴$ $a \in (6, \infty)$

Solution

Q.
The set of values of the parameter $' a'$ for which the function; $f (x) = 8 a x - a \sin 6 x - 7 x - \sin 5 x$ increases $\forall x \in R$ and has no critical points is

1 $[- 1, 1]$

2 $(- \infty, - 6)$

3 $(- \infty, - 6]$

4 $(6, \infty)$

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Solution

Q. The set of values of the parameter 'a' for which the function; f(x)=8ax-asin6x-7x-sin5x increases ∀x∈R and has no critical points is

1 [-1,1]

2 (-∞,-6)

3 (-∞,-6]

4 (6,∞)