Question

Need to find an approximate value for x in the equation x^3-e^x=-13/4 Lost on how to go about doing it

Answer 1

The appropriate choice of approach depends upon what course you're taking. I suspect you're beginning Calculus. Is that correct?

Answer 2

Actually Differential equations..but I am having a brain freeze on the process for solving this...I can approximate e as being 2.72

Answer 3

Remember Newton's Method?

Answer 4

No..but i will look it up.

Answer 5

"Newton's Method for Approximating Roots."

Answer 6

Do you remember using any other method for approximating the roots of an equation?

Answer 7

Calc 1 was 2 years ago...I am an older student (much older) so I my courses are spread out over time...thus I am having o go back and re teach some parts

Answer 8

I'd like to build on an approach that is familiar to you, if possible. Were I doing the problem myself, I'd definitely use Newton's method.

Answer 9

shall we go thru Newton's Method for approx. roots? or could you propose an approach more familiar?

Answer 10

I can try..always up for learning something new or forgotten

Answer 11

You're given \[x^3-e^x=-\frac{ 13 }{ 4 }\]

Answer 12

would u pls verify that this is correct?

Answer 13

The actual equation would be x^3-e^x +13/4 >= 0

Answer 14

Let's look at this as a function, f(x): \[f(x)=x^3-e^x+\frac{ 13 }{ 4 }\]

Answer 15

our task is to determine the value or values of x at which this function = 0. Can you agree with that?

Answer 16

Yes...

Answer 17

So am looking at 1- f(x) / f(x)' ? For the approximation?

Answer 18

Please find f '(x) now.

Answer 19

Yes. Apparently you have done this kind of approx. before.

Answer 20

3x^2-e^x

Answer 21

Have you a TI-84 calculator or similar?

Answer 22

No I was looking back at some notes and saw this..just now.

Answer 23

Yes

Answer 24

OK. Please, aritrarily, choose a beginning value (solution value) for x.
Interestingly, a random choice often works fine.

Answer 25

So say x =1?

Answer 26

Sure.

Answer 27

OK

Answer 28

Calculator redy?

Answer 29

.ok

Answer 30

Please type in the following:

\[1-(x^1-e^1+13/4)/(3(1)^2-e^1)\]

Answer 31

This follows your formula exactly.

Answer 32

ok

Answer 33

Your result?

Answer 34

-36.38387.....

Answer 35

I've obtained -4.437.
I'll do it again, and encourage you to do the same, until our results are equal.
Watch the parentheses carefully as you type in this formula.

Answer 36

surely is hard to type in the keying instructions.
How familiar are you with the TI-84?

Answer 37

ti -83 plus