Question

Q.26. The function f is strictly increasing in [a,b] if
A) f(x) <0 for x € [a,b]
B) f(x) >0 for x € [ab]
C) Both A) & B)
D) None of the above.​

Answer 1

Answer:

your correct answer is----(A)

Answer 2

Option B is correct

Correct question

The function f is strictly increasing in [a,b] if

A) f'(x) <0 for x € [a,b]

B) f'(x) >0 for x € [ab]

C) Both A) & B)

D) None of the above.

Given

• function f
• interval [a,b]

To find

• The correct options regarding the function

Solution

we are provided with a function and a closed interval a,b and asked to pick out the correct option regarding the increasing characteristic of the function

we know that a function is strictly increasing only if the slope of the cuve is positive or greater than zero.

that is the derivative or the slope in the case should be greater than zero, mathematically we can write the condition as follows,

f'(x) > 0 (slope positive)

here, f'(x) is that derivative of the function that represent the slope of the curve when the function is plotted on a graph.

For a function to be increasing, it is necessary that the above provided condition should be satisfied in all the points of the closed interval a,b.

It must be noted immediately that in this case, if the derivative of the function equal to zero the point is said to be critical point and if such a point the exist between the interval considered, we may not be able to say that the function is strictly increasing

Therefore, we can arrive at the conclusion that option B is correct.