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

Find the values of x for which the function f(x) = x3 – 6x2 – 36x + 7 is strictly increasing - Mathematics and Statistics

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

Find the values of x for which the function f(x) = x3 – 6x2 – 36x + 7 is strictly increasing

Advertisement Remove all ads

Solution

f(x) = x3 – 6x2 – 36x + 7

∴ f′(x) = 3x2 – 12x – 36

= 3(x2 – 4x – 12)

= 3(x – 6)(x + 2)

f(x) is strictly increasing, if f′(x) > 0

∴ 3(x – 6)(x + 2) > 0

∴ (x – 6)(x + 2) > 0

ab > 0 ⇔ a > 0 and b > 0 or a < 0 and b < 0

Either x – 6 > 0 and x + 2 > 0

or

x – 6 < 0 and x + 2 < 0

Case I: x – 6 > 0 and x + 2 > 0

∴ x > 6 and x > – 2

∴ x > 6

Case II: x – 6 < 0 and x + 2 < 0

∴ x < 6 and x < – 2

∴ x < – 2

Thus, f(x) is strictly increasing for x ∈ (−∞ −2) ∪ (6, ∞).

Concept: Increasing and Decreasing Functions
  Is there an error in this question or solution?
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×