A Function Is Given $U ( x ) = 4 \left( x ^ { 3 } - x \right)$

question 49

Essay

A function is given. (a) Find all the local maximum and minimum values of the function and the value of x at which each occurs
b) Find the intervals on which the function is increasing and on which the function is decreasing. State each answer correct to two decimal places. $U ( x ) = 4 \left( x ^ { 3 } - x \right)$

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Definitions:

Friedman-Phelps

An economic theory associated with Milton Friedman and Edmund Phelps, focusing on the natural rate of unemployment and the relationship between inflation and unemployment.

Actual Inflation

The real rate at which the general level of prices for goods and services is rising, and, subsequently, purchasing power is falling.

Natural Rate

The level of any economic factor, such as unemployment or interest rates, that is unaffected by short-term fluctuations and is determined by long-term factors.

Aggregate-Supply Curve

A curve that shows the quantity of goods and services that firms choose to produce and sell at each price level