Embibe Experts Solutions for Chapter: Application of Derivatives - I, Exercise 1: Exercise 1

The largest set of values of $x$ for which $x\ln x>x-1$ is

Set of all possible values of $k$ for which $f\left(x\right)=\sin x-\cos x-kx+b$ decreases for all real values of $x$, is

The angle which the perpendicular from the origin on the tangent makes with the $x$-axis for the curve whose parametric equation is $x=a{\sin }^3\theta , y=a{\cos }^3\theta$ is

Number of extreme as of $f\left(x\right)=3x^4-4x^3+6x^2+ax+b$, where $a, b\in R$, is
 

Equation of normal to the curve $y=x(2-x)$ at the point $(2,0)$is
 

If the tangent to the function $y=f\left(x\right)$ at $(3,4)$makes an angle of $\frac{3\mathrm{\pi }}{4}$ with the positive direction of $x$ -axis in anticlockwise direction, then $f^{\text{'}}\left(3\right)$ is

If function $f\left(x\right)=\cos \left|x\right|-2ax+b$ is strictly increasing function on whole number line, then the value of $a$ is

The set of values of a such that the equation $2x^2-2(2a+1)$$x+a(a-1)=0$ has roots$\alpha$ and $\beta$ satisfying $a<a<\beta$ is