Question
Question: Let the tangent to the graph of y = f(x) at the point x = a be parallel to x-axis and let f '(a – h...
Let the tangent to the graph of y = f(x) at the point x = a be parallel to x-axis and let
f '(a – h) > 0 and f ' (a + h) < 0 where h is a very small + ve
quantity. Then, the ordinate at x = a is -
A
A maximum
B
A minimum
C
Both a maximum and minimum
D
Neither maximum nor a minimum
Answer
A maximum
Explanation
Solution
We have f '(a – h) > 0 Ž f(x) is in left nbd to x = a
f '(a + h) < 0 Ž f(x) is Æ in Right nbd to x = a.
\ f(1) is local maximum.