For the function f(x)=(cos x)-x+1, x R, between the following two statements (S1) f(x)=0 for only one value of x in [0, π]. (S2) f(x) is decreasing in [0, (π)/2] and increasing in [(π)/2, π].

(A) Both (S1) and (S2) are incorrect.

(D) Both (S1) and (S2) are correct.

Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

JEE Main 2024 · 8 Apr, Morning shift · Q2735

JEE Main 20248 Apr, Morning shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

For the function

f(x)=(\cos x)-x+1, x \in \mathbb{R}

, between the following two statements (S1)

f(x)=0

for only one value of

x

[0, \pi]

. (S2)

f(x)

is decreasing in

\left[0, \frac{\pi}{2}\right]

and increasing in

\left[\frac{\pi}{2}, \pi\right]