Differential Calculus-2 Questions (6)

Consider $f(x) = \int \left(t + \frac{1}{t}\right) dt$ and $g(x) = f'(x)$ for $x \in \left[-3, -\frac{1}{2}\right]$. If P is a point on the curve $y = g(x)$ such that the tangent to this curve at P is parallel to a chord joining the points $\left(\frac{1}{2}, g\left(\frac{1}{2}\right)\right)$ and $(3, g(3))$ of the curve, then the coordinates of the point P

P and Q are two points on a circle of centre C and radius $a$, the angle PCQ being 20 then the radius of the circle inscribed in the triangle CPQ is maximum when

P and Q are two points on a circle of centre C and radius $a$, the angle PCQ being 20 then the radius of the circle inscribed in the triangle CPQ is maximum when

Let a function $f$ be defined as $f(x) = \begin{cases} \frac{|x-1|}{x^2+1} & \text{if } x > -1 \\ x^2 & \text{if } x \leq -1 \end{cases}$. Then the number of critical point(s) on the graph of this function is/are:

Consider $f(x) = \int \left(t + \frac{1}{t}\right) dt$ and $g(x) = f'(x)$ for $x \in \left[-3, -\frac{1}{2}\right]$. If P is a point on the curve $y = g(x)$ such that the tangent to this curve at P is parallel to a chord joining the points $\left(\frac{1}{2}, g\left(\frac{1}{2}\right)\right)$ and $(3, g(3))$ of the curve, then the coordinates of the point P

Let a function $f$ be defined as $f(x) = \begin{cases} \frac{|x-1|}{x^2+1} & \text{if } x > -1 \\ x^2 & \text{if } x \leq -1 \end{cases}$. Then the number of critical point(s) on the graph of this function is/are: