Question

Compare f(x) = x2 + 2x + 3 to a function that has a minimum value of 2.

Which statement is TRUE?
A) The minimum value for both functions is 2.
B)
The minimum value for f(x) = x2 + 2% + 3 is greater
than 2.
The minimum value for f(x) = * 24 * 3 is less than
2
D) %) = y2 + 24 + 3 has a maximum value of 2.

Answer 1

C and D

Explanation:

f(x) = x² + 2x + 3

Dy/dx = 2x + 2

At minimum

Dy/dx = 0

2x + 2 = 0

2x = -2

Divide both sides by 2

x = -2/2

x = -1

At maximum

y = x² + 2x + 3

y = (-1)² + 2(-1) + 3

y = 1 - 2 + 3

y = -1 + 3

y = 2

Which of the statement is true.

Option A is wrong because the minimum value of the first equation is -1 not 2

Option B is wrong because the minimum value of f(x) = x² + 2x + 3 is -1 which is less than 2 not greater than 2

Option C is correct because the minimum value of x² + 2x + 3 is -1 which is less than 2

Option D is correct because the maximum of f(x) = x² + 2x + 3 is 2