alleryStart learning →A function $f$ is strictly increasing on an interval if, throughout it:
- $f'(x) = 0$
- $f'(x) < 0$
- $f'(x) > 0$
- $f(x) > 0$
Show answer and solution
Correct answer: C. $f'(x) > 0$
A function is strictly increasing where its derivative is positive.
Indian Navy SSR Application of Derivatives — practice questions
Explore 26 free Application of Derivatives questions in Indian Navy SSR Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
Practise Application of Derivatives with Quill →Application of Derivatives questions and exercises with answers
Showing questions 1–26 of 26.
A function $f$ is strictly increasing on an interval if, throughout it:Read the answer and worked solution →What does the sign of f ′(x) tell you?Read the answer and worked solution →Complete the definition of a critical pointRead the answer and worked solution →Order the first derivative testRead the answer and worked solution →Match each sign change to its verdictRead the answer and worked solution →The second derivative testRead the answer and worked solution →True or false: maxima and minimaRead the answer and worked solution →Order the working rule for absolute maxima and minimaRead the answer and worked solution →Tap every point you must test for an absolute maximumRead the answer and worked solution →Local or absolute?Read the answer and worked solution →Complete the rate of change statementRead the answer and worked solution →The chain rule for related ratesRead the answer and worked solution →Assertion and reasonRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Spot the one that does not belongRead the answer and worked solution →Three of these are wrong. Find the one that holds.Read the answer and worked solution →True or false: increasing and decreasingRead the answer and worked solution →Flip and pair: symbol with meaningRead the answer and worked solution →Match each situation to the right toolRead the answer and worked solution →Tap every statement true of a local maximum at cRead the answer and worked solution →Reading the tests backRead the answer and worked solution →Which test is being described?Read the answer and worked solution →Assertion and reason: rates of changeRead the answer and worked solution →Spot the odd oneRead the answer and worked solution →Complete the second derivative testRead the answer and worked solution →True or false: scope of this chapterRead the answer and worked solution →
Worked practice questions
What does the sign of f ′(x) tell you?
Read exercise and reference answers
- Items
- Item
- f ′(x) > 0 throughout
- Category
- Increasing
- Item
- x₁ < x₂ gives f(x₁) < f(x₂)
- Category
- Increasing
- Item
- f ′(x) < 0 throughout
- Category
- Decreasing
- Item
- x₁ < x₂ gives f(x₁) > f(x₂)
- Category
- Decreasing
- Item
- f(x) = c for all x
- Category
- Constant
- Item
- f ′(x) = 0 throughout the interval
- Category
- Constant
- Categories
- Item
- Increasing
- Item
- Decreasing
- Item
- Constant
Your syllabus gives f ′(x) ≥ 0 on an interval as the test for increasing and f ′(x) ≤ 0 for decreasing.
Everything else in the chapter builds on reading that sign.
Source: syllabus Maths Part I, Ch 6 Application of Derivatives.
Complete the definition of a critical point
Read exercise and reference answers
- Missing parts
- Answer
- 0
- Choices
- 0
- 1
- undefined
- Answer
- not differentiable
- Choices
- not differentiable
- not continuous
- not defined
- Complete the statement
- A point c in the domain of f is a critical point if either f ′(c) = {0}, or f is {1} at c.
Your syllabus's definition covers two cases, and the second one is the one people forget. Source: syllabus Maths Part I, Ch 6 Application of Derivatives.
How to practise
- Choose a Application of Derivatives question and try to work out your answer.
- Open the question to check the correct answer and read its worked solution.
- Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.