CBSE (Science) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

Solution for Write the Interval in Which F(X) = Sin X + Cos X, X ∈ [0, π/2] is Increasing ? - CBSE (Science) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

Write the interval in which f(x) = sin x + cos x, x ∈ [0, π/2] is increasing ?

Solution

\[f\left( x \right) = \sin x + \cos x, x \in \left[ 0, \frac{\pi}{2} \right]\]

\[f'\left( x \right) = \cos x - \sin x\]

\[\text { For f(x) to be increasing, we must have}\]

\[f'\left( x \right) > 0\]

\[ \Rightarrow \cos x - \sin x > 0\]

\[ \Rightarrow \sin x < \cos x\]

\[ \Rightarrow \frac{\sin x}{\cos x} < 1\]

\[ \Rightarrow \tan x < 1\]

\[ \Rightarrow x \in [0, \frac{\pi}{4}]\]

  Is there an error in this question or solution?

APPEARS IN

Solution for question: Write the Interval in Which F(X) = Sin X + Cos X, X ∈ [0, π/2] is Increasing ? concept: Increasing and Decreasing Functions. For the courses CBSE (Science), PUC Karnataka Science, CBSE (Arts), CBSE (Commerce)
S
View in app×