Applications Of Derivatives – Tangents and Normal — Important Questions
Telangana Open School (TOSS) · Class 12 · Mathematics
42 important questions from Applications Of Derivatives – Tangents and Normal for Telangana Open School (TOSS) Class 12 Mathematics, with answers.
Interactive on Super Tutor
Studying Applications Of Derivatives – Tangents and Normal? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for important questions and more.
Free trial, no card needed.
Important Questions from Applications Of Derivatives – Tangents and Normal
The slope of the normal to a curve at a point is the negative reciprocal of the slope of the tangent.
Show answer
True
By definition, the normal is perpendicular to the tangent. If tangent slope is \( m \), normal slope is \( -\frac{1}{m} \).
For the curve \( y = \sin x \), what is the slope of the tangent at \( x = 0 \)?
Show answer
1
Differentiate: \( \frac{dy}{dx} = \cos x \). At \( x = 0 \), \( \cos 0 = 1 \).
The equation of the tangent to \( y = x^2 \) at \( (1, 1) \) is:
Show answer
y = 2x - 1
Slope at \( x = 1 \) is 2. Using point-slope: \( y - 1 = 2(x - 1) \Rightarrow y = 2x - 1 \).
The length of the subnormal to the curve \( y^2 = 4ax \) is constant.
Show answer
True
For \( y^2 = 4ax \), \( yy' = 2a \), so subnormal = \( |yy'| = 2a \), a constant.
+38 more questions on Applications Of Derivatives – Tangents and Normal (Telangana Open School (TOSS) Class 12 Mathematics)
Practise AllFrequently Asked Questions
What are the important topics in Applications Of Derivatives – Tangents and Normal for Telangana Open School (TOSS) Class 12 Mathematics?
How many important questions are there in Applications Of Derivatives – Tangents and Normal?
Sources & Official References
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Applications Of Derivatives – Tangents and Normal
Practice Quiz
Test yourself with a quick quiz
Revision Notes
Key points for last-minute revision
Formula Sheet
The chapter's formulas in one place
Chapter Summary
Understand the chapter at a glance
Concept Maps
See how topics connect
Study Plan
Step-by-step plan for this chapter
Flashcards
Quick-fire cards for active recall
Syllabus
What topics to cover
For serious students
Get the full Applications Of Derivatives – Tangents and Normal chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Telangana Open School (TOSS) Class 12 Mathematics. Free to start, no card needed.