Maxima and Minima of Functions of Two Variables — Study Resources & P…
Determination of maxima and minima for functions of two variables.
- Estimated study time: 30 minutes
Study resources
- Maxima & Minima of Two Variables + Lagrange Multipliers (Article) — Direct links to GP Sir's videos on maxima-minima of f(x,y) and Lagrange's method of undetermined multipliers, plus partial differentiation and multiple integrals.
- Maxima & Minima of Two Variables + Lagrange Multipliers (Video) — Complete engineering-maths playlist; contains the second-derivative test for two variables and constrained optimisation by Lagrange multipliers.
- Taylor's & Maclaurin's Series (Two Variables) (Article) — Authoritative reference for Taylor's theorem in two variables, maxima/minima tests and multiple integrals. Use for the precise two-variable formula.
- MIT OpenCourseWare — Multivariable Calculus (Article) — MIT multivariable-calculus materials covering partial derivatives, homogeneous-function ideas, Taylor expansions, extrema and Lagrange multipliers.
- MIT OpenCourseWare — Linear Algebra (Article) — MIT linear-algebra materials covering matrices, rank, elementary operations, eigenvalues/eigenvectors, Cayley-Hamilton-related concepts and diagonalization.
Maxima and Minima of Functions of Two Variables previous year questions
- (a) If $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$, then show that : $\nabla^2(r^m) = m(m - 1)r^{m-2}$. (b) Find the divergence and curl of the vector function…
- Verify whether the following statements are true or false. (i) The curve $y^2 = x^3$ has a node at the origin. (ii) The curve $r = a \cos 2\theta$ has two leav…
- (a) Verify Rolle's theorem for $f(x) = e^x(\sin x - \cos x)$ in $\left[\frac{\pi}{4}, \frac{5\pi}{4}\right]$. (b) Examine the function $f = xy(a - x - y)$ for…
- (a) Find the angle between the surfaces $x^2 + y^2 + z^2 = 9$ and $x^2 + y^2 - z = 3$ at the point $(2, -1, 2)$. (b) Show that $\text{div}(\text{curl } \vec{F}…
- (a) Express $\tan^{-1} Z$ into real and imaginary parts. (b) If $e^{i\theta} = \sinh(x + i y)$, show that $\sinh^4 x = \cos^3 \theta = \cos^4 y$.
Taught in these subjects
- ENGINEERING MATHEMATICS-I — BMAT11 · Government College of Engineering and Technology, Jammu
- ENGINEERING MATHEMATICS-1 — BMAT11 · Government College of Engineering and Technology, Jammu
- ENGINEERING MATHEMATICS-I — BMAT11 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BMAT11 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BST1101 · Government College of Engineering and Technology, Jammu
- Engineering Mathematics-I — BST1101 · Government College of Engineering and Technology, Jammu