Question

If f is decreasing in [a,b], its minimum and maximum values are respectively...... and......,Select correct option from the given options.
(a) f(a) and f(b)
(b) f(b) and f(a)
(c) f(a+b/2) and f(a)
(d) f(b) and f(a+b/2)

Answer 1

answer : option (b) f(b) and f(a)

concept : basically a function f is increasing. it means, for x > y ⇒f(x) > f(y), where x and y are points in its domain.

and function f is decreasing . it means, for x > y ⇒f(x) < f(y)

if any function, y = f(x) is strictly increasing in [a, b] then, maximum value of f(x) at x = b and minimum value of f(x) at x = a.

but function is strictly decreasing in [a,b] then, maximum value of f(x) at x = a

and minimum value of f(x) at x = b.

here, function f is decreasing in [a, b]

hence, maximum value at x = a i.e., f(a)

and minimum value at x = b i.e., f(b)