Derivatives, functions and finding tangent line

bagofchips123

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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.
 

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So what did you calculate is

[MATH]\dfrac{f(x + h) - f(x)}{h} = \text {WHAT?}[/MATH]
 
Nothing wrong with your first step.

[MATH]f(x) = x(4 - x) \implies f(x) = 4x - x^2.[/MATH]
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.

[MATH]f(x) = x(4 - x) \implies f(x) = 4x - x^2.[/MATH]
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.

[MATH]f(x) = x(4 - x) \implies f(x) = 4x - x^2.[/MATH]
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!
 
This is basic algebra

[MATH]f(x + h) = 4(x + h) - (x + h)^2.[/MATH]
Work it out.

EDIT OK i have waited 15 minutes. Going to bed.
 
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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
 
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.
 
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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
 
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.
 
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