Advertisements
Advertisements
प्रश्न
Find the maximum and minimum value, if any, of the following function given by g(x) = − |x + 1| + 3.
Advertisements
उत्तर
Given function g(x) = - |x + 1| + 3; g (3) ≤ 3∀ x ∈ R
Maximum value of -|x +1| = 0
Maximum value of g(x) = -|x + 1| + 3 = 0 + 3 = 3
occurs when x + 1 = 0, i.e., when x = -1.
Note that g(x) has no minimum value, for g (x) → a - ∞ as |x| ∞.
APPEARS IN
संबंधित प्रश्न
Find the approximate value of cos (89°, 30'). [Given is: 1° = 0.0175°C]
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) = (2x − 1)2 + 3.
Prove that the following function do not have maxima or minima:
g(x) = logx
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]`
Find the absolute maximum value and the absolute minimum value of the following function in the given interval:
f (x) = sin x + cos x , x ∈ [0, π]
A wire of length 28 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into a circle. What should be the length of the two pieces so that the combined area of the square and the circle is minimum?
Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is `8/27` of the volume of the sphere.
Show that the semi-vertical angle of the cone of the maximum volume and of given slant height is `tan^(-1) sqrt(2)`
The maximum value of `[x(x −1) +1]^(1/3)` , 0 ≤ x ≤ 1 is ______.
Find the maximum area of an isosceles triangle inscribed in the ellipse `x^2/ a^2 + y^2/b^2 = 1` with its vertex at one end of the major axis.
A ball is thrown in the air. Its height at any time t is given by h = 3 + 14t – 5t2. Find the maximum height it can reach.
Find the volume of the largest cylinder that can be inscribed in a sphere of radius ‘r’ cm.
Solve the following:
A rectangular sheet of paper of fixed perimeter with the sides having their lengths in the ratio 8 : 15 converted into an open rectangular box by folding after removing the squares of equal area from all corners. If the total area of the removed squares is 100, the resulting box has maximum volume. Find the lengths of the rectangular sheet of paper.
Determine the maximum and minimum value of the following function.
f(x) = 2x3 – 21x2 + 36x – 20
If x + y = 3 show that the maximum value of x2y is 4.
Max value of z equals 3x + 2y subject to x + y ≤ 3, x ≤ 2, -2x + y ≤ 1, x ≥ 0, y ≥ 0 is ______
If f(x) = 3x3 - 9x2 - 27x + 15, then the maximum value of f(x) is _______.
Twenty meters of wire is available for fencing off a flowerbed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is ______
Find the height of the cylinder of maximum volume that can be inscribed in a sphere of radius a.
The function `"f"("x") = "x" + 4/"x"` has ____________.
The maximum value of `[x(x - 1) + 1]^(2/3), 0 ≤ x ≤ 1` is
Read the following passage and answer the questions given below.
|
|
- Is the function differentiable in the interval (0, 12)? Justify your answer.
- If 6 is the critical point of the function, then find the value of the constant m.
- Find the intervals in which the function is strictly increasing/strictly decreasing.
OR
Find the points of local maximum/local minimum, if any, in the interval (0, 12) as well as the points of absolute maximum/absolute minimum in the interval [0, 12]. Also, find the corresponding local maximum/local minimum and the absolute ‘maximum/absolute minimum values of the function.
Let f: R → R be a function defined by f(x) = (x – 3)n1(x – 5)n2, n1, n2 ∈ N. Then, which of the following is NOT true?
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 ______.
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 ______.
The volume of the greatest cylinder which can be inscribed in a cone of height 30 cm and semi-vertical angle 30° is ______.
A rod AB of length 16 cm. rests between the wall AD and a smooth peg, 1 cm from the wall and makes an angle θ with the horizontal. The value of θ for which the height of G, the midpoint of the rod above the peg is minimum, is ______.
Find the maximum profit that a company can make, if the profit function is given by P(x) = 72 + 42x – x2, where x is the number of units and P is the profit in rupees.
Complete the following activity to divide 84 into two parts such that the product of one part and square of the other is maximum.
Solution: Let one part be x. Then the other part is 84 - x
Letf (x) = x2 (84 - x) = 84x2 - x3
∴ f'(x) = `square`
and f''(x) = `square`
For extreme values, f'(x) = 0
∴ x = `square "or" square`
f(x) attains maximum at x = `square`
Hence, the two parts of 84 are 56 and 28.
If x + y = 8, then the maximum value of x2y is ______.
Divide the number 100 into two parts so that the sum of their squares is minimum.
Find the point on the curve y2 = 4x, which is nearest to the point (2, 1).
A box with a square base is to have an open top. The surface area of box is 147 sq. cm. What should be its dimensions in order that the volume is largest?
If \[f\] has a maximum value at \[c\], what is \[c\] called?
Assume \[f'(c)=0\] and the second derivative exists at \[c\]. Which condition gives a local maximum?
Assume \[f'(c)=0\] and the second derivative exists at \[c\]. Which condition gives a local minimum?
For \[f(x)=3x^4+4x^3-12x^2+12\], what is \[f'(x)\]?
