f′(x)=4sin3xcosx−4cos3xsinx=−sin(4x).
Set f′(c)=0: sin(4c)=0⇒4c=nπ.
In (0,π/2), c=4π.
The value of C which satisfies Rolle's Theorem for f(x)=sin4x+cos4x in [0,2π]. Then C is :
Held on 15 Jun 2023 · Verified 13 Jul 2026.
5π
3π
4π
6π
Sign in to track your attempts and accuracy.
Sign in to keep a private note on this question. Nothing you write is ever public.
The derivative of x³ + 2x² - 5x + 1 is:
In which of the following interval the function $f(x) = x^x, x > 0$ is strictly increasing?
$\int \sin x \sin 2x \sin 3x dx$ is equal to
The differential equation representing the family of curves $y = Ax + \frac{B}{x}$, $x \neq 0$ where A and B are arbitrary constants, is given by
For the function $f(x) = -2x^3 + 3x^2 + 36x - 10$, which of the following is/are true? (A) $f$ is increasing in $(-\infty, -2)$ (B) $f$ is increasing in $(-2, 3)$ (C) $f$ is decreasing in $(-\infty, -2)$ (D) $f$ is decreasing in $(3, \infty)$ Choose the correct answer from the options given below:
Work through every CUET UG Calculus PYQ, year by year.