Find all the roots of the given function. Use preliminary analysis and graphing to find good initial approximations. f0x) = 4 In x-x+8x-2 The function has root(s) at x (Round to six decimal places as needed. Use a comma to separate answers as needed.)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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**Finding the Roots of the Function**

To determine the roots of the following function, apply preliminary analysis and graphical methods to obtain accurate initial approximations.

\[ f(x) = 4 \ln x - x^2 + 8x - 2 \]

**Roots Calculation**

The function has root(s) at \( x \approx \) 
\[ \_\_\_\_\_\_\_\_\_ \]
(Round to six decimal places as needed. Use a comma to separate answers as needed.)
Transcribed Image Text:**Finding the Roots of the Function** To determine the roots of the following function, apply preliminary analysis and graphical methods to obtain accurate initial approximations. \[ f(x) = 4 \ln x - x^2 + 8x - 2 \] **Roots Calculation** The function has root(s) at \( x \approx \) \[ \_\_\_\_\_\_\_\_\_ \] (Round to six decimal places as needed. Use a comma to separate answers as needed.)
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