## Applications of Derivatives: Tutorial: IITJEE Maths: Part II

Another set of “**easy to moderately difficult” **questions:

- The function decreases in the interval (a) (b) (c) (d) . There are more than one correct choices. Which are those?
- The function decreases in the interval (a) (b) (c) (d) . There is more than one correct choice. Which are those?
- For , satisfies the inequality: (a) (b) (c) (d) . There is more than one correct choice. Which are those?
- Suppose exists for each x and for every real number x. Then, (a) h is increasing whenever f is increasing (b) h is increasing whenever f is decreasing (c) h is decreasing whenever f is decreasing (d) nothing can be said in general. Find the correct choice(s).
- If , when , and , when . Then, (a) is increasing on (b) is continuous on (c) doesn’t exist (d) has the maximum value at . Find all the correct choice(s).
- In which interval does the function increase?
- Which is the larger of the functions and in the interval ?
- Find the set of all x for which .
- Let , if ; and, , if . If has local minimum at , then ?
- There are exactly two distinct linear functions (find them), such that they map and .

more later, cheers,

Nalin Pithwa.

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