Derivatives, functions and finding tangent line

bagofchips123

New member
Joined
Apr 11, 2021
Messages
14
Hi guys, im terribly stuck on this question and have been trying to solve it all day. Could someone please help me solve it, it would be greatly appreciated. Keep in mind i have been asked to use first principle.
 

Attachments

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
6,328
So what did you calculate is

\(\displaystyle \dfrac{f(x + h) - f(x)}{h} = \text {WHAT?}\)
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
6,328
How does your book define a first derivative?
 

bagofchips123

New member
Joined
Apr 11, 2021
Messages
14
So what did you calculate is

\(\displaystyle \dfrac{f(x + h) - f(x)}{h} = \text {WHAT?}\)
sorry my working wasnt included, however it is now posted. thankyou
 

bagofchips123

New member
Joined
Apr 11, 2021
Messages
14

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
6,328
Nothing wrong with your first step.

\(\displaystyle f(x) = x(4 - x) \implies f(x) = 4x - x^2.\)

My suggestion is that you deal with the Newton quotient before you worry about the limit and go step by step. I am going to use h rather than Delta x. (Makes no difference)

So what is f(x + h)? Work it out carefully.
 

bagofchips123

New member
Joined
Apr 11, 2021
Messages
14
Nothing wrong with your first step.

\(\displaystyle f(x) = x(4 - x) \implies f(x) = 4x - x^2.\)

My suggestion is that you deal with the Newton quotient before you worry about the limit and go step by step. I am going to use h rather than Delta x. (Makes no difference)

So what is f(x + h)? Work it out carefully.
[/
Nothing wrong with your first step.

\(\displaystyle f(x) = x(4 - x) \implies f(x) = 4x - x^2.\)

My suggestion is that you deal with the Newton quotient before you worry about the limit and go step by step. I am going to use h rather than Delta x. (Makes no difference)

So what is f(x + h)? Work it out carefully.
As you can see from my working i have tried to work out f(x+h), that is little help to me. if you could properly assist with solving the equation, which will in the future help me solve alternative equations that would be great!
 

JeffM

Elite Member
Joined
Sep 14, 2012
Messages
6,328
This is basic algebra

\(\displaystyle f(x + h) = 4(x + h) - (x + h)^2.\)

Work it out.

EDIT OK i have waited 15 minutes. Going to bed.
 
Last edited:

bagofchips123

New member
Joined
Apr 11, 2021
Messages
14
This is basic algebra

\(\displaystyle f(x + h) = 4(x + h) - (x + h)^2.\)

Work it out.

EDIT OK i have waited 15 minutes. Going to bed.
your help was useless
 

lex

Full Member
Joined
Mar 3, 2021
Messages
480
Hi guys, im terribly stuck on this question and have been trying to solve it all day. Could someone please help me solve it, it would be greatly appreciated. Keep in mind i have been asked to use first principle.
Your work is correct. The tangent line is (your final line): y=4

1620040765523.png
 

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
7,464

lookagain

Elite Member
Joined
Aug 22, 2010
Messages
2,764
Could someone please help me solve it, it would be greatly appreciated. Keep in mind i have been asked to use first principle.

Wherever you posted \(\displaystyle \ \Delta x^2, \ \) you should have written \(\displaystyle (\Delta x)^2 \ \) instead. The rest of the work appears to follow correct steps.

The numerator in your first line for the derivative should have looked like this
for consistency in the order of terms of the function (regardless that what you
wrote is the equivalent):

\(\displaystyle -(x + \Delta x)^2 \ + \ 4(x + \Delta x) \ - \ (-x^2 + 4x) \)


For one thing, this stresses proper order of substitution.
 
Last edited:

bagofchips123

New member
Joined
Apr 11, 2021
Messages
14
Wherever you posted \(\displaystyle \ \Delta x^2, \ \) you should have written \(\displaystyle (\Delta x)^2 \ \) instead. The rest of the work appears to follow correct steps.

The numerator in your first line for the derivative should have looked like this
for consistency in the order of terms of the function (regardless that what you
wrote is the equivalent):

\(\displaystyle -(x + \Delta x)^2 \ + \ 4(x + \Delta x) \ - \ (-x^2 + 4x) \)


For one thing, this stresses proper order of substitution.
thank you mate. i appreciate it
 

bagofchips123

New member
Joined
Apr 11, 2021
Messages
14
So you are saying that you cannot do basic algebra? In that case, you should not be taking a Calculus class.
So you are saying that you cannot do basic algebra? In that case, you should not be taking a Calculus class.
Fantastic advice, now that you mention it ill drop the class and not seek maths-related help on a maths-related problem!
 

HallsofIvy

Elite Member
Joined
Jan 27, 2012
Messages
7,464
Well, I was actually suggesting that you review algebra or even take a "Pre-Calculus" class but you know your abilities better than anyone else.
 
Top