Q. 1 A5.0( 1 Vote )

# Find the absolute maximum and the absolute minimum values of the following functions in the given intervals:

f(x) = 4x – x^{2}/2 in [–2, 45]

Answer :

given function is f(x) =

∴f'(x) = 4 – x

Now,

f'(x) = 0

4 – x = 0

x = 4

Then, we evaluate of f at critical points x = 4 and at the interval [ – 2, ]

f(4) = = 8

f(– 2) =

f() =

Hence, we can conclude that the absolute maximum value of f on [ – 2, 9/2] is 8 occurring at x = 4 and the absolute minimum value of f on [ – 2, 9/2] is – 10 occurring at x = – 2

Rate this question :

A metal box with a square base and vertical sides is to contain 1024 cm^{3}. The material for the top and bottom costs ` 5 per cm^{2} and the material for the sides costs ` 2.50 per cm^{2}. Find the least cost of the box.

Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is 6√3r.

RD Sharma - Volume 1Show that among all positive numbers x and y with x^{2} + y^{2} = r^{2}, the sum x + y is largest when x = y = .

Find the local maxima and local minima, of the function f(x) sin x – cos x, 0< x < 2π .Also, find the local maximum and local minimum values.

Mathematics - Board PapersProve that the semi-vertical angle of the right circular cone of given volume and least curved surface area is cot-1√2.

Mathematics - Board PapersProve that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is

Mathematics - Board Papers