0, then c is a point of ______. - Mathematics | Shaalaa.com" /> 0, then c is a point of ______. " /> 0, then c is a point of ______., Maxima and Minima" />
English

Let f have second derivative at c such that f′(c) = 0 and f"(c) > 0, then c is a point of ______. - Mathematics

Advertisements
Advertisements

Question

Let f have second derivative at c such that f′(c) = 0 and f"(c) > 0, then c is a point of ______.

Fill in the Blanks

Solution

Let f have second derivative at c such that f′(c) = 0 and f"(c) > 0, then c is a point of Local minima.

shaalaa.com
  Is there an error in this question or solution?
Chapter 6: Application Of Derivatives - Solved Examples [Page 134]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 6 Application Of Derivatives
Solved Examples | Q 26 | Page 134

RELATED QUESTIONS

Find the maximum and minimum value, if any, of the function given by f(x) = |x + 2| − 1.


Find the local maxima and local minima, if any, of the following function. Find also the local maximum and the local minimum values, as the case may be:

`h(x) = sinx + cosx, 0 < x < pi/2`


Find the absolute maximum value and the absolute minimum value of the following function in the given interval:

`f(x) =x^3, x in [-2,2]`


What is the maximum value of the function sin x + cos x?


Find two numbers whose sum is 24 and whose product is as large as possible.


Find two positive numbers x and y such that their sum is 35 and the product x2y5 is a maximum.


Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to \[ \frac{2}{3} \] of the diameter of the sphere.


Find the maximum and minimum of the following functions : f(x) = 2x3 – 21x2 + 36x – 20


Divide the number 20 into two parts such that sum of their squares is minimum.


Find the largest size of a rectangle that can be inscribed in a semicircle of radius 1 unit, so that two vertices lie on the diameter.


A box with a square base is to have an open top. The surface area of the box is 192 sq cm. What should be its dimensions in order that the volume is largest?


The profit function P(x) of a firm, selling x items per day is given by P(x) = (150 – x)x – 1625 . Find the number of items the firm should manufacture to get maximum profit. Find the maximum profit.


Show that among rectangles of given area, the square has least perimeter.


Show that the height of a closed right circular cylinder of given volume and least surface area is equal to its diameter.


Determine the maximum and minimum value of the following function.

f(x) = 2x3 – 21x2 + 36x – 20


Determine the maximum and minimum value of the following function.

f(x) = `x^2 + 16/x`


By completing the following activity, examine the function f(x) = x3 – 9x2 + 24x for maxima and minima

Solution: f(x) = x3 – 9x2 + 24x

∴ f'(x) = `square`

∴ f''(x) = `square`

For extreme values, f'(x) = 0, we get

x = `square` or `square`

∴ f''`(square)` = – 6 < 0

∴ f(x) is maximum at x = 2.

∴ Maximum value = `square`

∴ f''`(square)` = 6 > 0

∴ f(x) is maximum at x = 4.

∴ Minimum value = `square`


The maximum volume of a right circular cylinder if the sum of its radius and height is 6 m is ______.


Max value of z equals 3x + 2y subject to x + y ≤ 3, x ≤ 2, -2x + y ≤ 1, x ≥ 0, y ≥ 0 is ______ 


If R is the circum radius of Δ ABC, then A(Δ ABC) = ______.


The minimum value of the function f(x) = 13 - 14x + 9x2 is ______


A metal box with a square base and vertical sides is to contain 1024 cm3. The material for the top and bottom costs Rs 5/cm2 and the material for the sides costs Rs 2.50/cm2. Find the least cost of the box.


Maximum slope of the curve y = –x3 + 3x2 + 9x – 27 is ______.


The maximum value of `(1/x)^x` is ______.


If y = x3 + x2 + x + 1, then y ____________.


A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is ______.


If S1 and S2 are respectively the sets of local minimum and local maximum points of the function. f(x) = 9x4 + 12x3 – 36x2 + 25, x ∈ R, then ______.


The function g(x) = `(f(x))/x`, x ≠ 0 has an extreme value when ______.


The maximum distance from origin of a point on the curve x = `a sin t - b sin((at)/b)`, y = `a cos t - b cos((at)/b)`, both a, b > 0 is ______.


If x + y = 8, then the maximum value of x2y is ______.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×