Differentiation, Second Derivative, of Functions Problem

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Homework Help Overview

The problem involves finding the second derivative of the function f²(x) at x=3, given specific values for the function and its first and second derivatives at that point. The subject area is differentiation, specifically focusing on the application of the chain rule and product rule in calculus.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the application of the chain rule and product rule for differentiation. There is confusion regarding the correct form of the derivative for f²(x), with attempts to clarify the derivative expression.

Discussion Status

The discussion is ongoing, with some participants providing guidance on differentiation rules. There is a lack of consensus on the correct derivative expression, and multiple interpretations of the derivative are being explored.

Contextual Notes

Participants are working with specific values for the function and its derivatives, but there is uncertainty about how to apply differentiation rules correctly in this context.

Loppyfoot
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Homework Statement



Suppose f(3)=2 , f'(3)=5 , and f''(3)= -2 . Then d²/dx² (f²(x)) at x=3 is equal to ____?

A. -20
B. 20
C. 38
D. 42
E. 10


The Attempt at a Solution



I am confused about how to find the function to get the derivative from that function. Any Ideas? Thanks.
 
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You have two choices here: the chain rule and product rule.
 
So would the derive of f²(x)= 2f'(x) *1?
 
would that be the correct derivative?
 
Loppyfoot said:
would that be the correct derivative?

Nope. Remember that the chain rule gives that [f(g(x))]' = f'(g(x)) g'(x).
 

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