हिंदी

Find the Local Maxima and Local Minima, If Any, of the Following Functions. Find Also the Local Maximum and the Local Minimum Values, as the Case May Be: `F(X) = Xsqrt(1-x), X > 0`

Advertisements
Advertisements

प्रश्न

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

`f(x) = xsqrt(1-x), x > 0`

Advertisements

उत्तर

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 6: Application of Derivatives - Exercise 6.5 [पृष्ठ २३२]

APPEARS IN

एनसीईआरटी Mathematics Part 1 and 2 [English] Class 12
अध्याय 6 Application of Derivatives
Exercise 6.5 | Q 3.8 | पृष्ठ २३२

वीडियो ट्यूटोरियलVIEW ALL [5]

संबंधित प्रश्न

If `f'(x)=k(cosx-sinx), f'(0)=3 " and " f(pi/2)=15`, find f(x).


An open box is to be made out of a piece of a square card board of sides 18 cms by cutting off equal squares from the comers and turning up the sides. Find the maximum volume of the box.


A telephone company in a town has 5000 subscribers on its list and collects fixed rent charges of Rs.3,000 per year from each subscriber. The company proposes to increase annual rent and it is believed that for every increase of one rupee in the rent, one subscriber will be discontinued. Find what increased annual rent will bring the maximum annual income to the company.


Find the maximum and minimum value, if any, of the following function given by f(x) = −(x − 1)2 + 10 


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


Find the maximum and minimum value, if any, of the following function given by h(x) = x + 1, x ∈ (−1, 1)


Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 − 72x − 18x2.


It is given that at x = 1, the function x4− 62x2 + ax + 9 attains its maximum value, on the interval [0, 2]. Find the value of a.


Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.


A square piece of tin of side 18 cm is to made into a box without a top  by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible?


Of all the closed cylindrical cans (right circular), of a given volume of 100 cubic centimetres, find the dimensions of the can which has the minimum surface area?


The point on the curve x2 = 2y which is nearest to the point (0, 5) is ______.


The maximum value of `[x(x −1) +1]^(1/3)` , 0 ≤ x ≤ 1 is ______.


Divide the number 30 into two parts such that their product is maximum.


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.


Solve the following : Show that a closed right circular cylinder of given surface area has maximum volume if its height equals the diameter of its base.


Find the local maximum and local minimum value of  f(x) = x3 − 3x2 − 24x + 5


If f(x) = px5 + qx4 + 5x3 - 10 has local maximum and minimum at x = 1 and x = 3 respectively then (p, q) = ______.


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


A telephone company in a town has 500 subscribers on its list and collects fixed charges of Rs 300/- per subscriber per year. The company proposes to increase the annual subscription and it is believed that for every increase of Re 1/- one subscriber will discontinue the service. Find what increase will bring maximum profit?


An open box with square base is to be made of a given quantity of cardboard of area c2. Show that the maximum volume of the box is `"c"^3/(6sqrt(3))` cubic units


Find the dimensions of the rectangle of perimeter 36 cm which will sweep out a volume as large as possible, when revolved about one of its sides. Also, find the maximum volume.


The smallest value of the polynomial x3 – 18x2 + 96x in [0, 9] is ______.


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


The curves y = 4x2 + 2x – 8 and y = x3 – x + 13 touch each other at the point ______.


The combined resistance R of two resistors R1 and R2 (R1, R2 > 0) is given by `1/"R" = 1/"R"_1 + 1/"R"_2`. If R1 + R2 = C (a constant), then maximum resistance R is obtained if ____________.


The function `f(x) = x^3 - 6x^2 + 9x + 25` has


A wire of length 36 m is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is k (meter), then `(4/π + 1)`k is equal to ______.


Let P(h, k) be a point on the curve y = x2 + 7x + 2, nearest to the line, y = 3x – 3. Then the equation of the normal to the curve at P is ______.


If p(x) be a polynomial of degree three that has a local maximum value 8 at x = 1 and a local minimum value 4 at x = 2; then p(0) is equal to ______.


If the function y = `(ax + b)/((x - 4)(x - 1))` has an extremum at P(2, –1), then the values of a and b are ______.


If the point (1, 3) serves as the point of inflection of the curve y = ax3 + bx2 then the value of 'a ' and 'b' are ______.


Let f(x) = (x – a)ng(x) , where g(n)(a) ≠ 0; n = 0, 1, 2, 3.... then ______.


The lateral edge of a regular rectangular pyramid is 'a' cm long. The lateral edge makes an angle a. with the plane of the base. The value of a for which the volume of the pyramid is greatest, is ______.


If Mr. Rane order x chairs at the price p = (2x2 - 12x - 192) per chair. How many chairs should he order so that the cost of deal is minimum?

Solution: Let Mr. Rane order x chairs.

Then the total price of x chairs = p·x = (2x2 - 12x- 192)x

= 2x3 - 12x2 - 192x

Let f(x) = 2x3 - 12x2 - 192x

∴ f'(x) = `square` and f''(x) = `square`

f'(x ) = 0 gives x = `square` and f''(8) = `square` > 0

∴ f is minimum when x = 8

Hence, Mr. Rane should order 8 chairs for minimum cost of deal.


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


Determine the minimum value of the function.

f(x) = 2x3 – 21x2 + 36x – 20


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×