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`)

solve by quadratic formula 2x(x-1)=1-x

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

second derivative test 2x²+6x

Solution

Maximum(−√3, −4√3), Minimum(√3, 4√3)

Show Steps

Hide Steps

Solve by:

Find using the Second Derivative Test

Find using the Second Derivative Test

Find using the First Derivative Test

One step at a time

Second Derivative Test definition

Suppose that x=c is a critical point of f ′(c) such that f ′(c)=0
and that f ′′(x) is continuous in a region around x=c. Then,
If f ′′(c)<0 then x=c is a local maximum.
If f ′′(c)>0 then x=c is a local minimum.
If f ′′(c)=0 then test failed and x=c can be a local maximum, local minimum or neither.

f ′(x)=2x²−6x²

Find intervals: Increasing:−∞ <x<−√3, Decreasing:−√3<x<0, Decreasing:0<x<√3, Increasing:√3<x<∞

f ′′(x)=12x³

Check the sign of f ′′(x)=12x³ at each critical point

Check critical point x=−√3: Maximum(−√3, −4√3)

Check critical point x=√3: Minimum(√3, 4√3)

Maximum(−√3, −4√3), Minimum(√3, 4√3)

Solve instead

domain 2x²+6x

range 2x²+6x

inverse 2x²+6x

Examples

Related Symbolab blog posts

Practice Makes Perfect

Learning math takes practice, lots of practice. Just like running, it takes practice and dedication. If you want...

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 second derivative test 2x²+6x or choose from the options below

I want to solve something else

Solve by: Find using the First Derivative Test

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