EXAMPLE 2 Find the local minimum and maximum values of the function below #x)-3x4-8x3 - 90x* + 7 Video Example SOLUTION f(x) 12x3 - 24x2 -180x 12x(x - 5)(x 3) From the chart Interval 12xx -5 x+3 f(x) decreasing on (-co,-3) +increasing on (-3, 0) decreasing on (0, 5) +increasing on (5, co) x> 5 we see that f(x) changes from negative to posiive at -3, so f(-3) Similarly, f(x) changes from negative to positive at 5, so f(5)- And, f(0) - is a local minimum value by the First Derivative Test. is a local minimum value is a local maximum value because f(x) changes from positive to negative at 0
Show transcribed image text EXAMPLE 2 Find the local minimum and maximum values of the function below #x)-3x4-8x3 - 90x* + 7 Video Example SOLUTION f(x) 12x3 - 24x2 -180x 12x(x - 5)(x 3) From the chart Interval 12xx -5 x+3 f(x) decreasing on (-co,-3) +increasing on (-3, 0) decreasing on (0, 5) +increasing on (5, co) x> 5 we see that f(x) changes from negative to posiive at -3, so f(-3) Similarly, f(x) changes from negative to positive at 5, so f(5)- And, f(0) - is a local minimum value by the First Derivative Test. is a local minimum value is a local maximum value because f(x) changes from positive to negative at 0