
7-36 Calculus – Differentiation and Integration
When x = -1, y = -2.
When x = 1, y = 2.
Let us investigate the nature of y′ at the surrounding points of x.
For x < -1
If x = -2, then y′ is -ve.
If x = -3, then y′ is -ve.
Thus, y is decreasing for x < -1.
For x Î (-1, 1)
If x = -0.5, then y′ is +ve.
If x = 0, then y′ is +ve.
If x = 0.5, then y′ is +ve.
Thus, y is increasing for x Î (-1, 1).
For x > 1
If x = 2, then y′ is -ve.
If x = 3, then y′ is -ve.
Thus, y is decreasing for x > 1.
Therefore, the function is increasing for x Î (-1, 1) and decreasing for x < -1 and x > 1.
And f has absolute maximum y = 2 at x = 1 and absolute minimum y = -2 at x = -1.
3.