relative max / min

[craziebbygirl]

Hi I have the problem: F(X) = -2X^2 + 4X = 3

I found: F'(X) = -4X + 4

critical value is : -4X = -1 so X = 1

However my book gives 1 and 5 for answer I do not understand how they got a 5.

Thanks in advance!

 

[mmm4444bot]

… F(X) = -2X^2 + 4X = 3 <<< Is the last term in this polynomial supposed to be + 3 ?

I found: F'(X) = -4X + 4

critical value is : -4X = -1 so X = 1 <<< This is not worded properly. Critical values are not equations.

Additionally, the equation -4X = -1 is wrong. Perhaps, there is another typographical error.

The critical value is 1.



However my book gives 1 and 5 for answer …

What is the question for which the book gives 1 and 5 as the answer ?

If the question is Find the critical value(s) of function f and, if you've given us the correct definition for function f (i.e., a second-degree polynomial), then your book is wrong.

When we realize that relative extrema occur only at critical values, and we realize that the graph of function f is a parabola, then it's clear that there is only one critical value because a parabola has only one extreme value (i.e., the value at the vertex).

 

[craziebbygirl]

The question is find all relative extrema for the function. Also the last term is +3.

 

[mmm4444bot]

The question is find all relative extrema for the function …

Then you're not done.

The extreme value is not 1. It's f(1).

If the book reports the value 1 as a relative extrema, then the book is wrong. (Perhaps, the book actually asked for the critical value AND the extreme value. In this case, I could see how the answer section might list these values in order as 1, 5.)

Do you understand the question?

 

[craziebbygirl]

I do not understand where the 5 comes from I understand that the 1 is the critical value. I was thinking that you plug the critical value into the original function, but that does not give me 5.

 

[mmm4444bot]

… I [am] thinking that you plug the critical value into the original function, but that does not give me 5.

It gives me 5. Please show your work.

 

[craziebbygirl]

I see what I was doing wrong i was squaring the -2 instead of realizing that it would be -2 * 1^2 which would just be -2 + 4 + 3 which does equal 5.

Thank you for helping me!