Maxima AND Minima formulas

Every formula JEE Advanced expects you to know for Maxima AND Minima, with the variables spelled out. Free, no sign-up. Read it before a mock, not during one.

Practise these formulas 213 practice questions

Formulas: 32
Subject: Mathematics
Exam: JEE Advanced
No sign-in needed: ₹0

Maxima AND Minima, every formula

32 formulas, typeset and free. Print it, or keep it open beside your practice.

Absolute maximum
$f (x) \leq f (a) \forall x \in D$
Absolute minimum
$f (x) \geq f (a) \forall x \in D$
Local maximum
$f (x) \leq f (a) \forall x \in (a - h, a + h)$
Local minimum
$f (x) \geq f (a) \forall x \in (a - h, a + h)$
Necessary condition
$f^{'} (a) = 0 (critical point)$
First derivative test (max)
$f^{'} changes + \to - at a$
First derivative test (min)
$f^{'} changes - \to + at a$
Second derivative test (max)
$f^{'} (a) = 0, f^{''} (a) < 0$
Second derivative test (min)
$f^{'} (a) = 0, f^{''} (a) > 0$
nth derivative test
$f^{'} (a) = \dots = f^{(n - 1)} (a) = 0, f^{(n)} (a) \neq = 0$
n even → extremum
Global extremum on [a,b]
$compare f (critical pts) and f (a), f (b)$
Point of inflection
$f^{''} (x_{0}) = 0 and f^{''} changes sign$
Convex (concave up)
$f^{''} (x) > 0$
Concave (concave down)
$f^{''} (x) < 0$
Min of (x-a)(x-b)
$- \frac{( a - b ) ^{2}}{4}$
Max of a cos²x + b sin²x
$max = a, min = b (a > b)$
Min of a²sec²x + b²cosec²x
$(a + b)^{2}$
Min of a²sin²x + b²cosec²x
$2 ab$
Min of a cot x + b tan x
$2 ab$
Max of sinᵖθ cosᑫθ
$at θ = tan^{- 1} \frac{p}{q}$
Product max (fixed sum)
$sum = k \Rightarrow product max at \frac{k}{2}, \frac{k}{2}$
Sum of squares min (fixed sum)
$min at \frac{k}{2}, \frac{k}{2}$
Max rectangle in circle
$square of side 2 r$
Max triangle in circle
$equilateral of side 3 r$
Max sector area (fixed perimeter K)
$\frac{K ^{2}}{16}$
Least tangent-intercept (ellipse)
$a + b$
portion between axes
Max rectangle in ellipse
$2 ab$
Max isosceles triangle in ellipse
$\frac{3 3}{4} ab$
Open box from square sheet
$side removed = \frac{a}{6}$
Cone circumscribing sphere (max V)
$h = \frac{4 R}{3}, sin α = \frac{1}{3}$
Least triangle by line through (p,q)
$2 pq$
with the axes
Sum of side & hypotenuse (max area)
$angle = 6 0^{\circ}$

Know the Maxima AND Minima formulas. Now use them.

Formulas only stick when you apply them under time. Adaptive practice picks the concept you keep dropping marks on.

Create a free account All formula sheets

Join QuestPix, Today!

Get notified first, with exam & curriculum updates, course & test series launch offers, motivation & success stories and free learning resources recommended by toppers.

Maxima AND Minima formulas

Maxima AND Minima, every formula

Absolute maximum

Absolute minimum

Local maximum

Local minimum

Necessary condition

First derivative test (max)

First derivative test (min)

Second derivative test (max)

Second derivative test (min)

nth derivative test

Global extremum on [a,b]

Point of inflection

Convex (concave up)

Concave (concave down)

Min of (x-a)(x-b)

Max of a cos²x + b sin²x

Min of a²sec²x + b²cosec²x

Min of a²sin²x + b²cosec²x

Min of a cot x + b tan x

Max of sinᵖθ cosᑫθ

Product max (fixed sum)

Sum of squares min (fixed sum)

Max rectangle in circle

Max triangle in circle

Max sector area (fixed perimeter K)

Least tangent-intercept (ellipse)

Max rectangle in ellipse

Max isosceles triangle in ellipse

Open box from square sheet

Cone circumscribing sphere (max V)

Least triangle by line through (p,q)

Sum of side & hypotenuse (max area)

More JEE Advanced Mathematics formula sheets

Know the Maxima AND Minima formulas. Now use them.

Join QuestPix, Today!