Related LinksVideo Examples: Increasing-Decreasing Functions
Increasing Function
Definition Of Increasing Function
A function f is said to be increasing if f(a) > f(b) when a > b.
More About Increasing Function
The graph of an increasing function always goes up from left to right.
A function is increasing at all the points where its derivative is positive.
Video Examples: Increasing-Decreasing Functions
Example of Increasing Function
In figure, the curve is going up from left to right. Hence, the function is said to be increasing.
Solved Example on Increasing Function
Ques: Find the interval in which f(x) = 3x? - 54x2 + 14 increases.
Choices:
A. (- 3, 3)
B. (0, 8)
C. (0, 3) U (3, 8)
D. (- 3, 0) U (3, 8)
Correct Answer: D
Solution:
Step 1: Here f(x) = 3x? - 54x2 + 14 [Given function.]
Step 2: f '(x) = 12x? - 108x [Differentiate.]
Step 3: = 12x (x2 - 9) [Factorize.]
Step 4: = 12x (x - 3) (x + 3) [Factorize.]
Step 5: For x (x + 3)(x - 3) > 0, f ' (x) > 0
Step 6: For x ε (- 3, 0) U (3, 8), f ' (x) > 0 [Solve the inequality.]
Step 7: So, f(x) increases in (- 3, 0) U (3, 8).