Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 16 + 2x − x^2, [0, 5]

Step-by-step explanation:

To get the absolute maximum and minimum values of the function f(x) = 16 + 2x − x² n the given interval [0,5], we need to get the values of f(x) at the end points. The end points are 0 and 5.

at x = 0;

f(0) =  16 + 2(0) − 0²

f(0) = 16

at the other end point i.e at x = 5;

f(5) =  16 + 2(5) − 5²

f(5) = 16 + 10-25

f(5)= 26-25

f(5) = 1

The absolute minimum value is 1  and  occurs at x  = 5

The absolute maximum value is 16 and  occurs at x  = 0

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w