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

In summary, the conversation discusses a problem with finding the critical point of a given function in Calculus. The person has attempted to solve it but is stuck and asks for help. They are not familiar with bisection or Newton's method for solving the problem and ask for further explanation or resources. It is mentioned that this problem cannot be solved algebraically and an iterative method must be used. The conversation ends with suggestions for using bisection or Newton's method to solve the problem.
  • #1
jackchen
14
0

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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  • #2
Do you know bisection method? Newton's method?
 
  • #3
I'm afraid I don't. I'm very weak in Calculus, sorry!
 
  • #4
Do you know how I can solve this?
or where I can find a good explanation?

Thank you! =)
 
  • #5

1. What is "Stuck with Differentiation halfway"?

"Stuck with Differentiation halfway" is a phrase often used in the field of mathematics and science to describe a situation where a problem or equation cannot be fully differentiated using traditional methods.

2. Why does differentiation sometimes get stuck halfway?

This can happen when a function or equation is too complex or unconventional, making it difficult for traditional differentiation techniques to be applied. It can also occur when there are multiple variables involved or when the function is not continuous.

3. How can I determine if a function is stuck with differentiation halfway?

You can try differentiating the function using traditional methods and see if you are unable to reach a final solution. If you are unable to fully differentiate the function, it is likely that it is stuck with differentiation halfway.

4. What are some alternative methods for differentiating a function that is stuck halfway?

There are several alternative methods that can be used, such as implicit differentiation, logarithmic differentiation, and the chain rule. These methods can help to differentiate functions that are unconventional or have multiple variables.

5. Is being stuck with differentiation halfway a common problem in mathematics and science?

Yes, it is a common problem, especially when dealing with complex or unconventional functions. It is important for scientists and mathematicians to be aware of alternative differentiation methods in order to solve these types of problems.

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