Maharashtra State BoardHSC Arts 12th Board Exam
Advertisement Remove all ads

Examine the Function for Maximum and Minimum F(X) = X3 − 9x2 + 24x. - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

Examine the function for maximum and minimum f(x) = x3 − 9x2 + 24x.

Advertisement Remove all ads

Solution

f(x) = x3 − 9x2 + 24x

∴ f ′(x) = 3x2 − 18x + 24

∴ f ′′(x) = 6x − 18

Now, f ′(x) = 0

∴ 3x2 − 18x + 24 = 0

∴ x2 − 6x + 8 = 0

∴ (x – 4)(x – 2) = 0

∴ x = 2 or x = 4

For x = 2,

f ′′(2) = 6(2) − 18 = 12 − 18 = −6 < 0

∴ f is maximum at x = 2

∴ maximum value = f(2) = (2)3 − 9(2)2 + 24(2) = 8 − 36 + 48 = 20

For x = 4,

f "(4) = 6(4) −18 = 24 −18 = 6 > 0

∴ f is minimum at x = 4

∴ minimum value = f(4) = (4)3 − 9(4)2 + 24(4) = 64 − 144 + 96 = 16

Concept: Maxima and Minima - Introduction of Extrema and Extreme Values
  Is there an error in this question or solution?

APPEARS IN

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×