How Do You Find the Critical Point of f(x) = e^x - 5x^2 - ln(x)?

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Homework Help Overview

The discussion revolves around finding the critical point of the function f(x) = e^x - 5x^2 - ln(x) for x > 0. The original poster expresses difficulty in differentiating the function and determining the critical points.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to differentiate the function and has derived f'(x) = e^x - 10x - 1/x but is unsure how to proceed. Some participants question the definition of critical points and suggest considering where f'(x) is not defined.

Discussion Status

Participants are exploring different methods for finding critical points, including iterative methods like bisection and Newton's method. There is no explicit consensus on a single approach, but guidance has been offered regarding the nature of critical points.

Contextual Notes

The original poster indicates a lack of familiarity with calculus concepts, which may affect their ability to engage with the problem effectively.

jackchen
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Homework Statement



I'm stuck halfway in my differentiation.

The question is:
Suppose f(x) is the following function when x > 0, find the x-coordinate of the critical point of f(x).

Homework Equations



Equation = f(x) = e^x - 5x^2 - ln(x)

The Attempt at a Solution



I solved for: f'(x) = e^x - 10x - 1/x

From here on, I'm stuck. Help please?
Thank you! =)
 
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Do you know bisection method? Newton's method?
 
I'm afraid I don't. I'm very weak in Calculus, sorry!
 
Do you know how I can solve this?
or where I can find a good explanation?

Thank you! =)
 

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