The values of ‘K’ for which the point of minimum of the function f (x) = 1 + K2x – x3 satisfy the inequality belongs to:
∴ Using number line rule for (x + 2) (x + 3) as shown above.
or maximum/minimum let f’(x) = 0,
∴ f (x) is maximum at x = x1, and f (x) is minimum at x = x2.
Find the set of critical points of the function
Let f (x) = sin x – x on [0, π/2], find local maximum and local minimum.
Then find the value of ‘a’ for which f (x) has local minimum at x = 2.
Discuss maxima and minima.
A cubic f (x) vanishes at x = –2 and has relative maximum/minimum x = –1 and Find the cubic f (x).
Find the maximum and minimum value of
Use the function f (x) = x1/x, x > 0 to determine the bigger of the two numbers.
The maximum value of
then the maximum value of f (θ), is:
The values of a and b for which all the extrema of the function; is positive and the minimum is at the point are: