Find the Extrema of the Function on the Given Interval $\sin 4 x , 0 \leq x \leq \frac { \pi } { 2 }$

question 292

Multiple Choice

Find the extrema of the function on the given interval, and say where they occur.
- $\sin 4 x , 0 \leq x \leq \frac { \pi } { 2 }$

• A) local maxima: 1 at \(x = \frac { \pi } { 8 }\) and 0 at \(x = \frac { \pi } { 2 }\);
• local minima: 0 at \(x = 0\) and \(- 1\) at \(x = \frac { 3 \pi } { 8 }\)
• B) local maxima: 1 at \(x = \frac { \pi } { 8 }\) and 0 at \(x = \frac { \pi } { 2 }\);
• local minimum: \(- 1\) at \(x = \frac { 3 \pi } { 8 }\)
• C) local maxima: 1 at \(x = \frac { \pi } { 4 }\) and 0 at \(x = \frac { \pi } { 2 }\);
• local minima: 0 at \(x = 0\) and \(- 1\) at \(x = \frac { 3 \pi } { 8 }\)
• D) local maxima: 1 at \(x = \frac { \pi } { 8 }\) and 0 at \(x = \frac { \pi } { 4 }\);
• local minimum: 0 at \(x = 0\)

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Definitions:

Demand Equation

A mathematical representation expressing the relationship between the quantity of a good demanded and its price, along with other factors affecting demand.

Supply Equation

A mathematical expression that represents the relationship between the quantity of a good that producers are willing to sell and factors that affect this quantity like the price of the good.

Shortage/Surplus

A market condition where the quantity demanded is greater/smaller than the quantity supplied, leading to a scarcity/excess of goods.

Price Ceiling

A legally imposed maximum price on goods or services, preventing prices from rising above a certain level.