Does The Function X2 plus 4x-5 equals 0 Have A Minimum Or Maximum?

Answer 1

f(x) = x2 + 4x - 5 ( a minimum since the coefficient of x2 is positive, the parabola opens upward)

f'(x) = 2x + 4

f''(x) = 2

At a maximum or minimum, f'(x) = 0

2x + 4 = 0

2x = -4

x = -2

f(-2) = 4 - 8 - 5 = -9

The stationary point occurs at (-2, -9)

f''(-2) = 2

The second derivative is positive at this point, so the gradient is becoming more positive. This means that before this point the gradient was negative and after this point the gradient is positive, so the point is a minimum.