Solving f(x) and Finding A and B

  • Thread starter Weave
  • Start date
In summary, the conversation is about simplifying and finding derivatives using first principles. The first problem involves finding the derivative of a function and simplifying it to a specific form, while the second problem involves finding the derivative of a quadratic function in a specific form. The conversation also discusses strategies for solving these problems, including using the quotient rule and multiplying by a constant to get the desired form.
  • #1
Weave
143
0

Homework Statement


This problem is not hard at all its just that this stupid online homework program is a problem. Anyways,

f(x)=1/(5x+7)

The quotient:
f(7+h)+f(7)\h

This can be simplified to:
1\(A+Bh)

What is A & B
What is f'(7)?

Homework Equations



[tex]lim_{h\rightarrow0}\frac{\f(7+h)-f(7)}{h}[/tex]


The Attempt at a Solution



The derivative is easy to get.
The final form is [tex]\frac{-5}{210h+1764}[/tex]
How do I get it to:

[tex]\frac{1}{A+Bh}[\tex]
 
Last edited:
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  • #2
Why not multiply top and bottom by -1/5?
 
  • #3
but when I input B=210 and A=1764 it tells me I'm incorrect
 
  • #4
Well, you haven't multiplied them by -1/5. In order to get [tex]\frac{-5}{210h+1764}[/tex] into the required form, you need to multiply top and bottom by -1/5 (to get unity in the numerator).
 
  • #5
Ah..of coarse.
There is another problem that requires the form Ah^2 + B h + C.
f(x) = 2x^2 + 9 x + 4, find f'(2).

Now I got :
2h+17, A is 0, B is 2 but
when i input 17 for c it is incorrect. Why?
 
Last edited:
  • #6
Umm do you have to do it by first principles? It seems the quotient rule would work fine here.

For your 2nd problem, f'(2)=17, I don't see what the problem is.
 
  • #7
Gib Z said:
Umm do you have to do it by first principles? It seems the quotient rule would work fine here.

For your 2nd problem, f'(2)=17, I don't see what the problem is.

Well the question wants the form Ah^2+Bh+C
I know that
A=0
B=2
Shouldnt C=17? When i input that it is wrong.
 
  • #8
If not c=17, I don't understand what else it could be!
 

What is f(x)?

F(x) is a mathematical function that relates the input value, x, to an output value, also known as the dependent variable.

How do you solve for f(x)?

To solve for f(x), you will need to know the input value, x, and the function itself. You can then substitute the value of x into the function and solve for the output value, f(x).

What is the purpose of finding A and B in f(x)?

Finding A and B in f(x) allows you to determine the specific equation or pattern that relates the input value, x, to the output value, f(x). This can be helpful in understanding the behavior of the function and making predictions.

How do you find A and B in f(x)?

The process for finding A and B in f(x) will depend on the type of function given. In linear functions, you can use two points on the graph to solve for A and B. In exponential or logarithmic functions, you may need to use logarithms or other methods to solve for these values.

Why is it important to solve for f(x) and find A and B?

Solving for f(x) and finding A and B allows you to fully understand and analyze the behavior of a function. This information can be used to make predictions and solve real-world problems in various fields such as science, engineering, and economics.

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