( x ) = gives x = . Also P ( ) ′′ . So P ( ) ′′ Thus, x = is a point of maxima. Hence, the manufacturer can earn maximum profit, if he sells items.
Miscellaneous Exercise on Chapter . Show that the function given by log f x has maximum at x = e . . The two equal sides of an isosceles triangle with fixed base b are decreasing at the rate of cm per second.
How fast is the area decreasing when the two equal sides are equal to the base ? . Find the intervals in which the function f given by 4sin cos cos f x is (i) increasing (ii) decreasing. .
Find the intervals in which the function f given by f x ≠ is (i) increasing (ii) decreasing. . Find the maximum area of an isosceles triangle inscribed in the ellipse y a b with its vertex at one end of the major axis. .
A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is m and volume is m . If building of tank costs Rs per sq metres for the base and Rs per square metre for sides. What is the cost of least expensive tank? .
The sum of the perimeter of a circle and square is k , where k is some constant. Prove that the sum of their areas is least when the side of square is double the radius of the circle. . A window is in the form of a rectangle surmounted by a semicircular opening.
The total perimeter of the window is m. Find the dimensions of the window to admit maximum light through the whole opening. . A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle.
Show that the minimum length of the hypotenuse is a b . Find the points at which the function f