We've updated our
Privacy Policy effective December 15. Please read our updated Privacy Policy and tap

en

English

Upgrade

Good job!

Practice More

Type your Answer

`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

역함수 (x^2+4x-45)/(x^2+x-30)

Topic

Full pad

`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

π

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for inverse tangent line

See All

area

asymptotes

critical points

derivative

domain

eigenvalues

eigenvectors

expand

extreme points

factor

implicit derivative

inflection points

intercepts

inverse

laplace

inverse laplace

partial fractions

range

slope

simplify

solve for

tangent

taylor

vertex

geometric test

alternating test

telescoping test

pseries test

root test

Steps Examples

Generated by AI

extreme points 3x²y+y³−3x²−3y²+2

Solution

Minimum(0, 2), Maximum(0, 0), Saddle(1, 1), Saddle(−1, 1)

Show Steps

Hide Steps

Solution steps

One step at a time

Second Partial Derivative Test definition

Suppose that (x, y)=(a, b) is a critical point of f(x, y)
and D(x, y)=∂²f∂ x² ∂²f∂ y² −(∂²f∂ x∂ y )². Then,
If D(a, b) > 0 and ∂²f∂ x² <0 then the point (a, b) is a local maximum.
If D(a, b) > 0 and ∂²f∂ x² >0 then the point (a, b) is a local minimum.
If D(a, b)<0 then the point (a, b) is a saddle point.
If D(a, b)=0 then test failed and the point (a, b) can be a local maximum, local minimum, saddle or neither.

Find the critical points: (0, 2), (0, 0), (1, 1), (−1, 1)

∂²f∂ x² =6y−6

D(x, y)=(6y−6)²−36x²

Check the sign of at each critical point

Check critical point (0, 2): Minimum

Check critical point (0, 0): Maximum

Check critical point (1, 1): Saddle

Check critical point (−1, 1): Saddle

Minimum(0, 2), Maximum(0, 0), Saddle(1, 1), Saddle(−1, 1)

Solve instead

critical points 3x²y+y³−3x²−3y²+2

Examples

Related Symbolab blog posts

My Notebook, the Symbolab way

Math notebooks have been around for hundreds of years. You write down problems, solutions and notes to go back...

Popular topics

median calculator dot product calculator arc length calculator maclaurin series calculator z score calculator critical point calculator inequalities calculator range calculator determinant calculator second derivative calculator lcm calculator partial derivative calculator complete the square calculator distributive property calculator mixed fractions calculator Time Calculator gradient calculator triple integrals calculator partial fractions calculator indefinite integral calculator solve for x calculator double integral solver vector calculator Date Calculator vertex calculator binomial expansion calculator decimal to fraction calculator difference quotient calculator eigenvalue calculator piecewise functions calculator radius of convergence calculator roots calculator exponential function calculator interval of convergence calculator fractions divide calculator inflection point calculator expand calculator variance calculator fractions multiply calculator fourier series calculator foil calculator modulo calculator series convergence calculator linear algebra calculator

Chat with Symbo

Hi, ask a question about extreme points 3x²y+y³−3x²−3y²+2 or choose from the options below

Explain how to find extreme points of a function

Solve instead critical points 3x²y+y³−3x²−3y²+2

Cooking Calculators

Cooking Measurement Converter Cooking Ingredient Converter Cake Pan Converter More calculators

Fitness Calculators

BMI Calculator Calorie Calculator BMR Calculator More calculators

Notebook

View Full Notebook