Question

For y=1− x 2/4 , determine concavity and the x-values where points of inllection occur, Do not sketch the graph.

A The function is never concave down On which interval(s) is the function concave up?
1. The function is concave up on _________
2. The curve is never concave up Determine the inflection point(s)

Answer 1

The function y = 1 - x^2/4 is neither concave up nor concave down. There are no points of inflection.

Step-by-step explanation:

The concavity of a function can be determined by analyzing the second derivative of the function. To find the concavity of y = 1 - x^2/4, we need to find the second derivative and analyze its sign:

1. First, find the first derivative of y using the power rule:

y' = -2x/4 = -x/2

2. Next, find the second derivative by differentiating the first derivative:

y'' = -1/2

Since the second derivative, y'', is a constant (-1/2), the function is never concave up or concave down.

3. To find the x-values where the points of inflection occur, set the second derivative equal to zero and solve for x:

-1/2 = 0

There are no x-values that satisfy this equation, which means there are no points of inflection for the function y = 1 - x^2/4.