I don't know how to find the value

[sophie9]

sketch the graph of the function, using the curve-sketching guide
g(x)=4-3x-2x^3

I'm stuck at the step to find the y-intercept, determine the intervals where g is increasing and where g is decreasing, to find the relative extrema, determine the concavity of g and the inflection points of g.

Below is the steps that I have done so far.

I would appreciate every help and effort given. Thanks.

 

[topsquark]

Are you supposed to derive these values or read them off the graph that you were supposed to make?

-Dan

 

[sophie9]

Are you supposed to derive these values or read them off the graph that you were supposed to make?

-Dan

I suppose I need to derive these values from calculations and then sketch the graph with the values obtained.

 

[sophie9]

I suppose I need to derive these values from calculations and then sketch the graph with the values obtained.

Do you have any idea to get the value of the x-intercept? I get the answer of 0.88 from the calculator but I don't know how to write the formula. Thks for helping.

 

[JeffM]

This looks like a calculus problem Do you know anything about differential calculus?

The question does NOT ask you to find an exact value for any x-intercept so why go there before trying the things you were specifically asked to do. It is helpful in SKETCHING a curve to find any x-intercepts, but it is not necessary.

If you do not know calculus, I shall give you a hint.

What can you say about g(x) if x < 0? How about if x > 0. How about if x > 1.

 

[topsquark]

This looks like a calculus problem Do you know anything about differential calculus?

The question does NOT ask you to find an exact value for any x-intercept so why go there before trying the things you were specifically asked to do. It is helpful in SKETCHING a curve to find any x-intercepts, but it is not necessary.

If you do not know calculus, I shall give you a hint.

What can you say about g(x) if x < 0? How about if x > 0. How about if x > 1.

Ah! I read the OP wrong. I thought you were supposed to sketch it using a graphing program.

It's still a good idea, though. It will help you check your work.

-Dan

 

[JeffM]

Ah! I read the OP wrong. I thought you were supposed to sketch it using a graphing program.

It's still a good idea, though. It will help you check your work.

-Dan

It is a strange problem to see under algebra. And it may perhaps be a bit strange NOWADAYS to see a problem on curve sketching anywhere with graphing calculators and programs readily available.

So I guess that I’d reverse the process. Look at the curve from a calculator and then explain why it makes sense, which is what you were thinking.