List of top Mathematics Questions on Application of derivatives asked in COMEDK UGET

Let \(f:\mathbb{R}\to\mathbb{R}\) be defined by \[ f(x)=x^3-3x+1 \] Then the function \(f\) is:
If the function \( f(x) = \mu \sin x + \frac{1}{3} \sin 3x \) has its derivative equal to zero at \( x = \frac{\pi}{3} \), then the value of \( \mu \) is __________.
Let \( f(x) = x\sqrt{4ax - x^2, \; a > 0 \) then \( f'(x) \) at \( x = 2a \) is:}
The curve \( 4y = 3x^4 - 2x^2 \) attains
The least value of \( a \) such that the function \( x^2 + ax + 1 \) is increasing on \([1,2]\) is