- #1
s883
- 5
- 0
Homework Statement
Could anyone explain me how to solve this?
Homework Equations
f(x) =
1/x2 + 4x + 9 + x4 , f’”’(-2) =
Understanding Differential Calculus: Solving Homework Equations
- Thread starter s883
- Start date
Could anyone explain me how to solve this?
f(x) =
1/x2 + 4x + 9 + x4 , f’”’(-2) =
- #2
Saladsamurai
- 3,009
- 7
Hello s883! 
It means to take the 4th derivative of the given function f(x) and then evaluate the resulting expression at x = -2. And I would probably put calculus questions in the calculus forum for next time 
It means to take the 4th derivative of the given function f(x) and then evaluate the resulting expression at x = -2. And I would probably put calculus questions in the calculus forum for next time - #3
HallsofIvy
Science Advisor
Homework Helper
- 42,895
- 984
I assume you mean f(x) = 1/x^2 + 4x + 9 + x^4= x^{-2}+ 4x+ 9+ x^4.
Can you find f'(x) using the "power rule" ((x^n)'= n x^{n-1})?
What about f'' and f'''?
Now do f''''.
Can you find f'(x) using the "power rule" ((x^n)'= n x^{n-1})?
What about f'' and f'''?
Now do f''''.
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Hello,
This is the attachment, the steps to solution are pretty clear. I guess there is a mistake on the highlighted part that prompts this thread.
Ought to be ##3^{n+1} (n+2)-6## and not ##3^n(n+2)-6##. Unless i missed something, on another note, i find the first method (induction) better than second one (method of differences).
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