Final answer:
To find the maximum and minimum values of the function f(x) = 2x^2 + 4x - 2, we can use calculus.
The minimum value is -2, and there is no maximum value.
Step-by-step explanation:
To find the maximum and minimum values of the function f(x) = 2x^2 + 4x - 2, we can use calculus.
First, we need to find the critical points by taking the derivative of the function and setting it equal to zero.
The derivative of f(x) is f'(x) = 4x + 4. Setting it equal to zero, we get 4x + 4 = 0.
Solving for x, we find that x = -1.
Next, we can use the second derivative test to determine whether these critical points are local minimum or maximum.
The second derivative of f(x) is f''(x) = 4, which is positive.
This means that x = -1 is a local minimum. Since there are no more critical points, this is the only extreme point of the function.
Therefore, the minimum value of f(x) is f(-1) = 2(-1)^2 + 4(-1) - 2 = -2.
There is no maximum value for this function since it continues to increase without bound as x approaches positive or negative infinity.