- #1
Torshi
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Homework Statement
See attachment - Question3
Homework Equations
The Attempt at a Solution
Not sure. I believe it's an easy plug and chug, but I could be wrong. I'm having trouble where to begin
Dick said:Sure plug and chug part b). Then part c) says to take a guess. Part d) says to verify it using the definition of derivative. Where are you stuck?
Torshi said:Part B: I did a similar one earlier, but alright so I'm using the g(x) equation right?
Double check:
So to get the value for 1.9 for the table I plug that number into this equation
5(1.9)^2+3(1.9)-4 - 5(2)^2 + 3(2) - 4 / (1.9-2)
Dick said:Ok. You aren't really using enough parentheses to indicate what you mean, but I'll trust you know. What do you get?
Torshi said:I got for question C - a number around 23.
The values I got for the table is in order from left to right: 22.5, 22.95, 23, 23, 23.05, 23.5
I need help for question D: I'm not familiar with the chain rule
Dick said:Ok, so you must have a pretty good idea for c). Why do you think you need a chain rule for d)?
Torshi said:Not sure, a friend told me - he may be wrong.
It says to calculate the IRC at x=2, do I just plug in 2 for 5(x)^2+3X-4 ?
Dick said:The IRC is the limit of g(x) as x->2, isn't it? That's what part b) was on about. g(x) is a difference quotient for f(x). What do limits of difference quotients have to do with derivatives? Check back to the definition of derivative.
Torshi said:a derivative is a function changing due to a different input or also how one quantity is changing due to another quantity.
Dick said:That's vague. The definition of f'(a) is limit x->a of (f(x)-f(a))/(x-a). Don't you have that definition someplace?
Torshi said:Yes, it's on the THQ question.
The reason why I'm sort of lost on these questions is 1.) I just started calc and 2.) We only covered 2 sections so far barely going over any problems. Matter of a fact our first problem section is tom w/ a classroom quiz over this material that he hasn't even covered fully.
Sorry for my lack of knowledge regarding this material. This is my last question and the packet is due tomorrow.
As for your question - yes i have it - not in classroom notes because he didn't go over it. But there is a question in the packet that involves the difference quotient and I solved it since it I knew it from college alg.
I'm still unsure for this last part. My 3rd class for calc is tom so we literally started a week ago.
Dick said:All ok. Part b) is asking you to compute values of (f(x)-f(2))/(x-2) for values of x that get close to 2. The closer x gets to 2 the closer you should be to the IRC. You should have guessed that the IRC is 23. To find it analytically you need to compare that with f'(2). Do you know how to find the derivative of f(x)=5x^2+3x-4 and put in x=2?
Torshi said:Does it involve dy/dx? Which is the chain rule then plug in 2 at the end?
Dick said:Yes, but no chain rule. It's just differentiating really. Can you differentiate 5x^2, 3x or 4? Just checking what you know.
Torshi said:I got 10X +3
10(2) +3 = 23 IRC
I wasn't even taught this, but figured it out. Is this a precal thing?
Dick said:No, it's a full calculus thing. The precalculus thing would have been to derive lim x->2 (f(x)-f(2))/(x-2) from first principles. Any idea how to do that? Not having taken precalc is not going to help. But try and tough it out.
Torshi said:No idea how to do that. Did I get the right answer though?
And yea I'ma try. I really need to. This is my last semester in order to graduate ;/
Dick said:It's the right answer. The derivative of 5x^2+3x-4 is 10x+3. It's nice to know how to really derive things, but if it's the last semester just try and bluff your way through. Good luck!
Torshi said:Thanks, I appreciate the help! And I'll do my best to do so!
An IRC function problem involves using the Iterative Refinement Method (IRC) to find the root of a function. This method involves repeatedly refining an initial guess until a desired level of accuracy is achieved.
The purpose of solving an IRC function problem is to find the root of a function, which is the value of the independent variable that results in a value of 0 for the function. This is useful in various areas of science, such as physics and engineering, for solving equations and finding important values.
To solve an IRC function problem, you must first choose an initial guess for the root and then use the IRC method to refine that guess until the desired level of accuracy is achieved. This typically involves using a computer program or calculator to perform the necessary calculations.
The IRC method is advantageous because it can be used to find the root of a function to a desired level of accuracy, even if the function is complex or does not have a closed-form solution. It is also a relatively efficient method, requiring fewer iterations compared to other methods.
Yes, there are some limitations to using the IRC method. It may not converge to the root if the initial guess is too far from the actual root or if the function has multiple roots. It also requires a good initial guess, which may be difficult to determine for some functions.