Question

Which function has the lowest minimum value, and what are its coordinates?

A. Function 1 has the lowest minimum value, and its coordinates are (−1, −3).
B. Function 1 has the lowest minimum value, and its coordinates are (0, 1).
C. Function 2 has the lowest minimum value, and its coordinates are (−1, 0).
D. Function 2 has the lowest minimum value, and its coordinates are (0, 2).

Answer 1

A. Function 1 has the lowest minimum value, and its coordinates are (−1, −3).

Explanation:

To find the minimum value for f(x), set its first derivative to 0 and solve for x.

First derivative of f(x) is

f'(x) = 8x + 8 + 0 = 8x + 8

Setting this equal to 0 gives

8x + 8 = 0

8x = -8

x = -1

Plugging in this value for x in 4x² + 8x + 1 gives

f(x) = 4(-1)² + 8(-1) = 4 · 1 - 8 + 1

= 4 - 8 + 1

-4 + 1

= -3

So minimum for f(x) occurs at (-1, -3)

For g(x) the minimum is 0 and is at x = -1

So f(x) has minimum of -3 at x = -1

g(x) has minimum of 0 and occurs at x = -1

Answer:

A. Function 1 has the lowest minimum value, and its coordinates are (−1, −3).