The number of local extremum points of the function f(x)=e sin x+2 sin x+x-4 in (0, (π/2)) is [Note: [ k ] and operatornamesgn( k ) denotes greatest integer function and signum function of k respectively.]

Question

The number of local extremum points of the function f(x)=e sin x+2 sin x+x-4 in (0, (π/2)) is [Note: [ k ] and operatornamesgn( k ) denotes greatest integer function and signum function of k respectively.] (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

f prime(x)=e sin x ⋅ cos x+2 cos x+1>0 for x ∈(0, (π/2)) No local extremum points of the function

Q. The number of local extremum points of the function $f (x) = e^{s i n x} + 2 sin x + x - 4$ in $(0, \frac{π}{2})$ is
[Note: $[k]$ and $sgn (k)$ denotes greatest integer function and signum function of k respectively.]

0

1

2

3

$f^{'} (x) = e^{s i n x} \cdot cos x + 2 cos x + 1 > 0$ for $x \in (0, \frac{π}{2})$
No local extremum points of the function

Q. The number of local extremum points of the function f(x)=esinx+2sinx+x−4 in (0,2π​) is [Note: [k] and sgn(k) denotes greatest integer function and signum function of k respectively.]

0

1

2

3

f′(x)=esinx⋅cosx+2cosx+1>0 for x∈(0,2π​) No local extremum points of the function

Q. The number of local extremum points of the function $f (x) = e^{s i n x} + 2 sin x + x - 4$ in $(0, \frac{π}{2})$ is
[Note: $[k]$ and $sgn (k)$ denotes greatest integer function and signum function of k respectively.]

$f^{'} (x) = e^{s i n x} \cdot cos x + 2 cos x + 1 > 0$ for $x \in (0, \frac{π}{2})$
No local extremum points of the function