JEE · Maths · Application of Derivatives doubts
12 doubts found
How do I find the dimensions that give the maximum area (or minimum material) — a real optimisation problem?
Turn the requirement into a single-variable function using the constraint.
A ladder slides down a wall — how fast is the top falling when I know how fast the base moves? (related rates)
The ladder length L is fixed, so x² + y² = L², where x is the base distance and y the height.
How does the derivative tell me where a function is rising or falling (useful for graphs and trends)?
The sign of the first derivative gives the direction.
Can I use derivatives to estimate a value like √26 quickly without a calculator?
Yes — linear approximation.
What does “Critical points” actually mean in Application of Derivatives, and why does it matter for JEE?
at a maximum or minimum of a smooth function the derivative is zero (the tangent is flat).
I keep getting “Critical points” questions wrong in Application of Derivatives. What's the trap?
thinking every point where f'(x)=0 is a maximum.
What does “Second-derivative test” actually mean in Application of Derivatives, and why does it matter for JEE?
at a critical point, f''>0 means a local minimum (cup up) and f''<0 means a local maximum (cap down).
I keep getting “Second-derivative test” questions wrong in Application of Derivatives. What's the trap?
confusing which sign of f'' gives a maximum.
What is the difference between increasing function and decreasing function?
A function is increasing where f'(x) > 0 (rising) and decreasing where f'(x) < 0 (falling); f'(x) = 0 marks turning points.
What is the difference between local maximum and local minimum?
At a local maximum the function stops rising and turns down (f''<0); at a local minimum it stops falling and turns up (f''>0).
When do I use dy/dt = (dy/dx)(dx/dt) in Application of Derivatives, and what does it mean?
chain rule for related rates.
When do I use f(x+δx) ≈ f(x) + f'(x)·δx in Application of Derivatives, and what does it mean?
linear approximation using the derivative.