INCREASING AND DECREASING FUNCTIONS: 1. Steps for working rule : i) Find f’(x) in factor form. ii) f’(x) = 0 and find the roots. iii) If there are roots ,then divide the real ‘n’ number line R into (n+1 ) disjoint open intervals . iv) Find the sign of f’(x) in each of the above intervals . v) f(x) is increasing or decreasing in the intervals when f’(x) is positive or negative respectively Tips and Techniques :- If the coefficient of the highest is +ve then the rightmost interval in the Real Line is +ve & the other intervals from right to left get alternatively signed. The given function is increasing in +ve signed intervals and decreasing in the signed –ve intervals. If the coefficient of the highest power is -ve then the rightmost interval in the Real Line is -ve & the other intervals from right to left get alternatively signed. The given function is increasing in +ve signed intervals and decreasing in the signed –ve intervals. SAMPLE QUESTIONS AND SOLUTION: Find the intervals in the function f given by is a) strictly increasing b) strictly decreasing Find the intervals in which the function f given by is strictly increasing or strictly decreasing. SOLUTION: Find the intervals in which the function f given by is a) strictly increasing b) strictly decreasing
INCREASING AND DECREASING FUNCTIONS: 1. Steps for working rule : i) Find f’(x) in factor form. ii) f’(x) = 0 and find the roots. iii) If there are ‘n’ roots ,then divide the real number line R into (n+1 ) disjoint open intervals . iv) Find the sign of f’(x) in each of the above intervals . v) f(x) is increasing or decreasing in the intervals when f’(x) is positive or negative respectively Tips and Techniques :- If the coefficient of the highest is +ve then the rightmost interval in the Real Line is +ve & the other intervals from right to left get alternatively signed. The given function is increasing in +ve signed intervals and decreasing in the –ve signed intervals. If the coefficient of the highest power is -ve then the rightmost interval in the Real Line is -ve & the other intervals from right to left get alternatively signed. The given function is increasing in +ve signed intervals and decreasing in the –ve signed intervals. SAMPLE QUESTIONS AND SOLUTION: Find the intervals in the function f given by is a) strictly increasing b) strictly decreasing Find the intervals in which the function f given by is strictly increasing or strictly decreasing. SOLUTION: Find the intervals in which the function f given by is a) strictly increasing b) strictly decreasing
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