Question
The value of 'c' in Lagrange's mean value theorem for 
in [0, 2] is
- 0
- 1
- 2/3
- 3/2
Hint:
Lagrange mean value theorem states that for any two points on the curve there exists a point on the curve such that the tangent drawn at this point is parallel to the secant through the two points on the curve.
The correct answer is: 2/3
Given : is a polynomial
We know that polynomials are continuous and differentiable in their range
Simplify f(x) for ease of calculation
Related Questions to study
The equation 
represents
The equation represents
The polar equation of the circle whose end points of the diameter are 
and 
is
The polar equation of the circle whose end points of the diameter are and is
The radius of the circle 
is
The radius of the circle is
The adjoining figure shows the graph of 
Then –
The adjoining figure shows the graph of Then –
Graph of y = ax2 + bx + c = 0 is given adjacently. What conclusions can be drawn from this graph –
Here we can see that the graph was given to us and us to take out the conclusion from that since we have the options available so I would suggest you to always start to check from the options because by the use of options we can see how easily we concluded this question.
Graph of y = ax2 + bx + c = 0 is given adjacently. What conclusions can be drawn from this graph –
Here we can see that the graph was given to us and us to take out the conclusion from that since we have the options available so I would suggest you to always start to check from the options because by the use of options we can see how easily we concluded this question.
For the quadratic polynomial f (x) = 4x2 – 8kx + k, the statements which hold good are
For the quadratic polynomial f (x) = 4x2 – 8kx + k, the statements which hold good are
The graph of the quadratic polynomial y = ax2 + bx + c is as shown in the figure. Then :
The roots (also called as zeros, y = 0) of the quadratic equation 
are given by x = 
. The quantity 
is called the discriminant of the equation and determines the nature of its roots.
If ≥ 0, the roots are real.
If = 0, the roots are real and equal.
If < 0, the roots are complex and conjugates of each other.
The graph of the quadratic polynomial y = ax2 + bx + c is as shown in the figure. Then :
The roots (also called as zeros, y = 0) of the quadratic equation are given by x = . The quantity is called the discriminant of the equation and determines the nature of its roots.
If ≥ 0, the roots are real.
If = 0, the roots are real and equal.
If < 0, the roots are complex and conjugates of each other.
The greatest possible number of points of intersections of 8 straight line and 4 circles is :
The students can make an error if they don’t know about the formula for calculating the number of points as mentioned in the hint which is as follows
The number point of intersection between two lines can be counted by finding the number of ways in which two lines can be selected out of the lot as two lines can intersect at most one point.
The number point of intersection between two circles can be counted by finding the number of ways in which two circles can be selected out of the lot multiplied by 2 as two circles can intersect at most two points.
The number point of intersection between two circles can be counted by finding the number of ways in which one circle and one line can be selected out of the lot multiplied by 2 as one circle and one line can intersect at most two points.
The greatest possible number of points of intersections of 8 straight line and 4 circles is :
The students can make an error if they don’t know about the formula for calculating the number of points as mentioned in the hint which is as follows
The number point of intersection between two lines can be counted by finding the number of ways in which two lines can be selected out of the lot as two lines can intersect at most one point.
The number point of intersection between two circles can be counted by finding the number of ways in which two circles can be selected out of the lot multiplied by 2 as two circles can intersect at most two points.
The number point of intersection between two circles can be counted by finding the number of ways in which one circle and one line can be selected out of the lot multiplied by 2 as one circle and one line can intersect at most two points.
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even position ?
Here we have obtained the total number of 9 digit numbers using the given digits. While finding the number of ways to arrange the odd digits in 5 even places, we have divided the 4! by 2! because the digit 3 were occurring two times and the digit 5 were occurring 2 times. Here we can make a mistake by conserving the number of even digits 4 and the number of odd digits 5, which will result in the wrong answer.
How many different nine digit numbers can be formed from the number 223355888 by rearranging its digits so that the odd digits occupy even position ?
Here we have obtained the total number of 9 digit numbers using the given digits. While finding the number of ways to arrange the odd digits in 5 even places, we have divided the 4! by 2! because the digit 3 were occurring two times and the digit 5 were occurring 2 times. Here we can make a mistake by conserving the number of even digits 4 and the number of odd digits 5, which will result in the wrong answer.
on the line 
is
is
and perpendicular to 
is
is
is
