Find the equation of the tangent line (Can someone check my work?)

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SUMMARY

The equation of the tangent line to the function g(x) = arctan(x) + ln(x) at x = 1 is correctly given as y - π/4 = 3/2(x - 1). While the final answer is accurate, the discussion emphasizes the importance of showing the work leading to the derivative g'(x) and the tangent line formula. Without this, verification of the solution's correctness is not possible, highlighting the need for detailed problem-solving steps in mathematical discussions.

PREREQUISITES
  • Understanding of derivatives, specifically g'(x) for g(x) = arctan(x) + ln(x)
  • Knowledge of the formula for the tangent line at a point, y - f(a) = f'(a)(x - a)
  • Familiarity with the properties of arctangent and natural logarithm functions
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Calculate the derivative g'(x) for g(x) = arctan(x) + ln(x)
  • Practice deriving the tangent line formula for various functions
  • Explore the implications of showing work in calculus problems
  • Review common mistakes in finding tangent lines and how to avoid them
USEFUL FOR

Students studying calculus, educators teaching derivative concepts, and anyone interested in improving their problem-solving skills in mathematics.

shamieh
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Find the equation of the tangent line to g(x) = arctan(x) + ln(x) @ x = 1

$$y - \frac{\pi}{4} = \frac{3}{2}(x - 1)$$
 
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Looks good to me. :D
 
shamieh said:
Find the equation of the tangent line to g(x) = arctan(x) + ln(x) @ x = 1

$$y - \frac{\pi}{4} = \frac{3}{2}(x - 1)$$

Your answer is indeed correct, but as no actual work is shown, we cannot verify that you didn't just happen to "guess" the right answer (although you probably didn't).

Things a teacher might want to see included in your answer:

1) What is g'(x)?

2) What is the formula for the tangent line to g(x) at x = a?

The correct two answers to the questions I have listed above are actually more important than "the final answer".
 
Deveno said:
Your answer is indeed correct, but as no actual work is shown...

This is an excellent point. If you answer happened to be incorrect, we would not have been able to address where you made any errors.
 

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