Advertisements
Advertisements
Question
f(x) = cos x, 0 < x < \[\pi\] .
Solution
\[\text { Given: } \hspace{0.167em} f\left( x \right) = \cos x\]
\[ \Rightarrow f'\left( x \right) = - \sin x\]
\[\text { For a local maximum or a local minimum, we must have }\]
\[f'\left( x \right) = 0\]
\[ \Rightarrow - \sin x = 0\]
\[ \Rightarrow \sin x = 0\]
\[ \Rightarrow x = 0 \ or \ \pi\]
Since \[0 < x < \pi\] none is in the interval \[\left( 0, \pi \right)\] .
APPEARS IN
RELATED QUESTIONS
f(x) = - (x-1)2+2 on R ?
f(x) = | sin 4x+3 | on R ?
f(x) = \[\frac{1}{x^2 + 2}\] .
f(x) = sin 2x, 0 < x < \[\pi\] .
`f(x)=sin2x-x, -pi/2<=x<=pi/2`
f(x) =\[x\sqrt{1 - x} , x > 0\].
f(x) =\[\frac{x}{2} + \frac{2}{x} , x > 0\] .
f(x) = x4 \[-\] 62x2 + 120x + 9.
`f(x) = 2/x - 2/x^2, x>0`
f(x) = xex.
f(x) = \[x^3 - 2a x^2 + a^2 x, a > 0, x \in R\] .
Find the absolute maximum and minimum values of the function of given by \[f(x) = \cos^2 x + \sin x, x \in [0, \pi]\] .
Find the absolute maximum and minimum values of a function f given by `f(x) = 12 x^(4/3) - 6 x^(1/3) , x in [ - 1, 1]` .
Determine two positive numbers whose sum is 15 and the sum of whose squares is maximum.
Divide 64 into two parts such that the sum of the cubes of two parts is minimum.
How should we choose two numbers, each greater than or equal to `-2, `whose sum______________ so that the sum of the first and the cube of the second is minimum?
Given the sum of the perimeters of a square and a circle, show that the sum of there areas is least when one side of the square is equal to diameter of the circle.
Find the largest possible area of a right angled triangle whose hypotenuse is 5 cm long.
A square piece of tin of side 18 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of the square to be cut off so that the volume of the box is maximum? Find this maximum volume.
Show that the height of the cylinder of maximum volume that can be inscribed a sphere of radius R is \[\frac{2R}{\sqrt{3}} .\]
Find the point on the curve y2 = 4x which is nearest to the point (2,\[-\] 8).
An open tank is to be constructed with a square base and vertical sides so as to contain a given quantity of water. Show that the expenses of lining with lead with be least, if depth is made half of width.
The strength of a beam varies as the product of its breadth and square of its depth. Find the dimensions of the strongest beam which can be cut from a circular log of radius a ?
A straight line is drawn through a given point P(1,4). Determine the least value of the sum of the intercepts on the coordinate axes ?
A particle is moving in a straight line such that its distance at any time t is given by S = \[\frac{t^4}{4} - 2 t^3 + 4 t^2 - 7 .\] Find when its velocity is maximum and acceleration minimum.
Write the maximum value of f(x) = \[x + \frac{1}{x}, x > 0 .\]
Write the minimum value of f(x) = xx .
The maximum value of x1/x, x > 0 is __________ .
For the function f(x) = \[x + \frac{1}{x}\]
The sum of two non-zero numbers is 8, the minimum value of the sum of the reciprocals is ______________ .
The function f(x) = \[\sum^5_{r = 1}\] (x \[-\] r)2 assumes minimum value at x = ______________ .
The least and greatest values of f(x) = x3\[-\] 6x2+9x in [0,6], are ___________ .
f(x) = \[\sin + \sqrt{3} \cos x\] is maximum when x = ___________ .
If 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 ______________ .
f(x) = 1+2 sin x+3 cos2x, `0<=x<=(2pi)/3` is ________________ .
The minimum value of x loge x is equal to ____________ .
