AP WORLD HISTORY FINAL pick any of the 3 prompts
PROMPT:

2. By the period 1200–1450 CE, the Silk Roads had long been established as a prominent trading route connecting Asia, the Middle East, and Europe.

Develop an argument that evaluates the extent to which patterns of interaction along the Silk Roads changed from 1200 to 1450 CE.

3. In the period 1450–1700 CE, many European countries made advancements in transoceanic exploration.

Develop an argument that evaluates the extent to which European exploration around 1500 CE changed the way in which empires facilitated trade.

4. In the period from 1900 CE to the present, the world faced multiple global conflicts that had a profound influence on world politics.

Develop an argument that evaluates the extent to which the end of World War II in 1945 brought major changes to world politics.

               

Answerresponsibility law;

Answer:     the interval on which the curve is concave up is  (-∞, -1/2)======    we find the interval where this curve is concave up by finding the interval in which the 2nd derivative is positive.differentiate the curve equation with respect to x    let the function f denote be the anti-derivative of the inside expression, i.e. a function such that .then use the fundamental theorem of calculus:     differentiate again to get second derivative. we can use chain rule with 1/x as the outside function and 1 + x + x² as the inside function    find critical numbers of the second derivative. these numbers are where the 2nd deriv. is undefined or zero.where the 2nd derivative is zero: set (d²y/dx²) to equal 0 and solve for x    where the 2nd derivative is undefined: if the denominator is equal to zero, the derivative will be undefeined. attempting to solve the equation    1 + x + x² = 0results in a discriminant of      meaning that the equal 1 + x + x² = 0 has no real solutions and therefore will never equal zero.======our only critical number is x = -1/2.this forms two intervals to test the sign for: (-∞, -1/2) and (-1/2, ∞)test values into the 2nd derivative for (-∞, -1/2)if we try x = -1, we get      so the since the 2nd derivative of the curve is positive on the interval  (-∞, -1/2), the curve is concave up on (-∞, -1/2)test values into the 2nd derivative for (-1/2, ∞)if we try x = 0, we get      so the since the 2nd derivative of the curve is positive on the interval  (-∞, -1/2), the  curve is concave down on (-∞, -1/2).the interval on which the curve is concave up is  (-∞, -1/2)

The answer would be c.