A video-streaming Web site keeps count of the number of times each video has been played since it was first added to the site. The count is updated each time a video is played and is displayed next to each video to show its popularity. At one time, the count for the most popular video was about two million. Sometime later, the same video displayed a seven-digit negative number as its count, while the counts for the other videos displayed correctly. Which of the following is the most likely explanation for the error?
a. The count for the video became larger than the maximum value allowed by the data type used to store the count.
b. The software used to update the count failed when too many videos were played simultaneously by too many users.
c. The mathematical operations used to calculate the count caused a rounding error to occur.
d. The software used to update the count contained a sampling error when using digital data to approximate the analog count.

The first answer is b. then the second one is a

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)

Cis the answer i pretty sure