# Derivatives, functions and finding tangent line

#### bagofchips123

##### New member
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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#### JeffM

##### Elite Member
So what did you calculate is

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

#### JeffM

##### Elite Member
How does your book define a first derivative?

#### bagofchips123

##### New member
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
How does your book define a first derivative?
basically by utilising the formula you provided

#### JeffM

##### Elite Member
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
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
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.

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#### bagofchips123

##### New member
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.

#### lex

##### Full Member
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

#### HallsofIvy

##### Elite Member
So you are saying that you cannot do basic algebra? In that case, you should not be taking a Calculus class.

#### lookagain

##### Elite Member
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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#### bagofchips123

##### New member
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
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
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.