Question

Find local maximum or minimum of the function: f(x)= (x + 1)^2(x - 3) Local maximum point= ( , ) Local maximum value= Local minimum point = ( , ) Local minimum value=

Answer 1

f ( x ) = ( x – 3) 2 – 4; the minimum value is –4

Explanation:

Given the function f ( x ) = x 2 – 6 x + 5, write an equivalent form of the function that reveals the minimum or maximum value of the function and state the minimum or maximum value.

f ( x ) = ( x – 3) 2 – 4; the minimum value is –4

( This The correct question to answer?) can't deleted..

Answer 2

Answer: Local Max = (-1, 0)

Local Min = (1, -8)

Explanation:

f(x) = (x + 1)² (x - 3)

Step 1: Find the zeros

(x + 1)² = 0 --> x = -1 (multiplicity of 2)

(x - 3) = 0 --> x = 3

Step 2: Find the Vertices

x = -1 --> (multiplicity is even which means this is a vertex)

The midpoint between x = -1 and x = 3 is x = 1

Step 3: Find the Local Max and Local Min

Use the x-value above to find the y-values

f(-1) = 0 because it is a zero

f(1) = (1 + 1)² (1 - 3)

= 2²(-2)

= 4(-2)

= -8

Conclusion:

(-1, 0) is the Local Max bigger y-value

(1, -8) is the Local Min smaller y-value