SUMMARY
The equation of the tangent line to the function y=e^(-2x) at the point (1,e^-2) can be determined by first differentiating the function to find its slope at that point. The derivative f'(x) = -2e^(-2x) leads to f'(1) = -2e^-2, which provides the slope of the tangent line. Using the point-slope form of the equation, y - e^-2 = -2e^-2(x - 1) yields the final equation of the tangent line.
PREREQUISITES
- Understanding of calculus, specifically differentiation
- Familiarity with exponential functions
- Knowledge of the point-slope form of a line
- Basic algebra skills for manipulating equations
NEXT STEPS
- Study differentiation techniques for exponential functions
- Learn about the point-slope form of linear equations
- Explore applications of tangent lines in calculus
- Review the properties of the exponential function y=e^u
USEFUL FOR
Students studying calculus, mathematics educators, and anyone interested in understanding tangent lines and their applications in exponential functions.