How is the shape of a quartic function different from the shape ofa cubic function? a quadratic function?

stratsticks57jl
2022-07-31
Answered

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dtal50

Answered 2022-08-01
Author has **10** answers

A quadratic function means its a parabola. A quartic functionis similar in shape to the quadratic graph. remember the equationfor quadratic functions ax^{2}+bx+c. Always helpful toremember! You can always differenitate from the rest just byremembering it!

Also think about what the function looks like to you. Aquadratic function opens up if its positive and it opens down if its negative.

A quadratic function differes from a cubic function forseveral reasons. 1, a cubic graph goes through the origin (0,0) andveers right, into the first quadrant. And from the bottom it veersleft into the third quadrant. Parabolas stay within the 1 and 2ndquadrants and 3 and 4th quadrants.

Also think about what the function looks like to you. Aquadratic function opens up if its positive and it opens down if its negative.

A quadratic function differes from a cubic function forseveral reasons. 1, a cubic graph goes through the origin (0,0) andveers right, into the first quadrant. And from the bottom it veersleft into the third quadrant. Parabolas stay within the 1 and 2ndquadrants and 3 and 4th quadrants.

Ruby Briggs

Answered 2022-08-02
Author has **3** answers

The shape of a quartic function is similar to a quadraticequation. It is different from the cubic function because itdoes not have an inflection point.

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Prove that $|\left|x\right|-|y||\le |x-y|$

I've seen the full proof of the Triangle Inequality$|x+y|\le \left|x\right|+\left|y\right|$ .

However, I haven't seen the proof of the reverse triangle inequality:

$|\left|x\right|-|y||\le |x-y|$ .

Would you please prove this using only the Triangle Inequality above?

Thank you very much.

I've seen the full proof of the Triangle Inequality

However, I haven't seen the proof of the reverse triangle inequality:

Would you please prove this using only the Triangle Inequality above?

Thank you very much.

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Consider the function $f\left(x\right)=2{x}^{3}+9{x}^{2}-108x+3,-6\le x\le 4$ .

Thus function has an absolute minimum value equal to

and an absolute maximum value equal to

Thus function has an absolute minimum value equal to

and an absolute maximum value equal to

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Use Vietas

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I am a web developer who is trying to understand Machine learning.

Solving a set of linear equations is a fundamental problem in maths. I understand that there exist efficient matrix based algorithms to compute the solution.

Now, to solve a set of non-linear equations is tough it seems and there aren't any algorithms to solve them.

My question is why is non-linearity such a big hazard in mathematics? Is it because obtaining a closed form solution of non-linear equation is not possible? (I am also vague about what closed form means, I think closed form is anything for which we can exactly write a formula.)

In particular, how is non-linearity connected to optimization problems and why can't we just take the derivative of the equation and solve it; in all cases. I think the answer to this lies in my previous question, i.e. we can't actually solve the non-linear equations we get by taking the derivative and setting it to zero.

Solving a set of linear equations is a fundamental problem in maths. I understand that there exist efficient matrix based algorithms to compute the solution.

Now, to solve a set of non-linear equations is tough it seems and there aren't any algorithms to solve them.

My question is why is non-linearity such a big hazard in mathematics? Is it because obtaining a closed form solution of non-linear equation is not possible? (I am also vague about what closed form means, I think closed form is anything for which we can exactly write a formula.)

In particular, how is non-linearity connected to optimization problems and why can't we just take the derivative of the equation and solve it; in all cases. I think the answer to this lies in my previous question, i.e. we can't actually solve the non-linear equations we get by taking the derivative and setting it to zero.