Advertisements
Advertisements
प्रश्न
The maximum value of the function f(x) = `logx/x` is ______.
विकल्प
e
`1/e`
e2
`1/e^2`
Advertisements
उत्तर
The maximum value of the function f(x) = `logx/x` is `bb(1/e)`.
APPEARS IN
संबंधित प्रश्न
Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is `(4r)/3`. Also find maximum volume in terms of volume of the sphere
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:
f(x) = sinx − cos x, 0 < x < 2π
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 both the maximum value and the minimum value of 3x4 − 8x3 + 12x2 − 48x + 25 on the interval [0, 3].
What is the maximum value of the function sin x + cos x?
Find two positive numbers whose sum is 16 and the sum of whose cubes is minimum.
A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is the maximum possible?
Show that the right circular cylinder of given surface and maximum volume is such that is heights is equal to the diameter of the base.
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 maximum value of `[x(x −1) +1]^(1/3)` , 0 ≤ x ≤ 1 is ______.
Show that a cylinder of a given volume, which is open at the top, has minimum total surface area when its height is equal to the radius of its base.
Choose the correct option from the given alternatives :
If f(x) = `(x^2 - 1)/(x^2 + 1)`, for every real x, then the minimum value of f is ______.
Solve the following : Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is `(2"R")/sqrt(3)`. Also, find the maximum volume.
Determine the maximum and minimum value of the following function.
f(x) = 2x3 – 21x2 + 36x – 20
A rod of 108 m long is bent to form a rectangle. Find it’s dimensions when it’s area is maximum.
The maximum volume of a right circular cylinder if the sum of its radius and height is 6 m is ______.
If R is the circum radius of Δ ABC, then A(Δ ABC) = ______.
The maximum and minimum values for the function f(x) = 4x3 - 6x2 on [-1, 2] are ______
Find all the points of local maxima and local minima of the function f(x) = `- 3/4 x^4 - 8x^3 - 45/2 x^2 + 105`
If x is real, the minimum value of x2 – 8x + 17 is ______.
The function f(x) = 2x3 – 3x2 – 12x + 4, has ______.
Find the maximum profit that a company can make, if the profit function is given by P(x) = 41 + 24x – 18x2.
Find the volume of the largest cylinder that can be inscribed in a sphere of radius r cm.
The coordinates of the point on the parabola y2 = 8x which is at minimum distance from the circle x2 + (y + 6)2 = 1 are ____________.
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 ____________.
For all real values of `x`, the minimum value of `(1 - x + x^2)/(1 + x + x^2)`
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.
A function f(x) is maximum at x = a when f'(a) > 0.
Let f(x) = (x – a)ng(x) , where g(n)(a) ≠ 0; n = 0, 1, 2, 3.... then ______.
A cone of maximum volume is inscribed in a given sphere. Then the ratio of the height of the cone to the diameter of the sphere is ______.
The sum of all the local minimum values of the twice differentiable function f : R `rightarrow` R defined by
f(x) = `x^3 - 3x^2 - (3f^('')(2))/2 x + f^('')(1)`
The maximum value of f(x) = `logx/x (x ≠ 0, x ≠ 1)` is ______.
If f(x) = `1/(4x^2 + 2x + 1); x ∈ R`, then find the maximum value of f(x).
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.
A metal wire of 36 cm long is bent to form a rectangle. Find its dimensions when its area is maximum.
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.
The shortest distance between the line y - x = 1and the curve x = y2 is
If \[\mathrm{A}+\mathrm{B}=\frac{\pi}{2}\] then the maximum value of cosA.cosB is
If \[f\] has a maximum value at \[c\], what is \[c\] called?
A maximum or minimum value of \[f\] is called a(n) _____.
For \[f(x)=3x^4+4x^3-12x^2+12\], what is \[f''(x)\]?
For \[f(x)=3x^4+4x^3-12x^2+12\], what conclusion follows at \[x=0\]?
For \[f(x)=3x^4+4x^3-12x^2+12\], what conclusion follows at \[x=1\]?

