Question

Tangent line to e⁻ˣ at given point

A) Factoring polynomials
B) Computing definite integrals
C) Finding tangent lines to a curve
D) Evaluating trigonometric functions

Answer 1

To find the tangent line to the function e^-x at the point t = 25s, we can take the derivative of the function and evaluate it at that point. The slope of the tangent line is -e^-25, and we can use the point-slope form to find the equation of the tangent line.

Step-by-step explanation:

The tangent line to the function e-x at the point t = 25 s can be found by taking the derivative of the function and evaluating it at that point. The derivative of e-x is -e-x. So, at t = 25 s, the slope of the tangent line is -e-25. To find the equation of the tangent line, we can use the point-slope form: y - y1 = m(x - x1). Plugging in the values, we get: y - e-25 = -e-25(x - 25).