Maxima and Minima in Calculus - Practice Questions & MCQ

Let $f(x)=x^3-x^2+x$ then number of points which are either local maxima or local minima is ?

If m and M are the minimum and the maximum values of

 then M−m is equal to :

The maximum volume (in cu.m) of the right circular cone having a slant height of 3 m is:

Let the tangents drawn to the circle, $x^2+y^2=16$ from the point $P(0, h)$ meet the $x$ axis at points A and B. If the area of $\triangle A P B$ is minimum, then n is equal to :

 If x= -1 and x = 2 are extreme points of   then 

Let   be such that the function f given by

has extreme values at x = –1 and x =  2.

Statement 1: f has a local maximum at x = –1 and at x = 2.

Statement 2 : .

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side=x units and a circle of radius=r units.  If the sum of the areas of the square and the circle so formed is minimum, then :

Which of the following graphs represents local maximaa at x = a

The function $f(x)=2 x+3(x)^{\frac{2}{3}}, x \in \mathbb{R}$, has

$\mathrm{f\left ( x \right )= x^{3}-3x+4}$ has local minimum at