Question

Find an equation for the tangent line to y=(x²)e−²ˣ at the point x=0.

a) y=x²
b) y=2x
c) y= −2x
d) y=0

Answer 1

To find the equation of the tangent line to the function y=(x²)e(-2x) at x=0, use derivatives to find the slope and the point-slope form of a linear equation to determine the equation of the tangent line.

Step-by-step explanation:

The equation for the tangent line to the function y=(x²)e(-2x) at the point x=0 can be found using the concept of derivatives. To find the equation of the tangent line, we need to find the slope of the function at the point (0, y). The slope of the tangent line is given by the derivative of the function evaluated at x=0.

The derivative of y=(x²)e(-2x) can be found using the product rule and the chain rule. After finding the derivative, plug in x=0 to find the slope. Then, use the point-slope form of a linear equation to determine the equation of the tangent line.

The equation of the tangent line to y=(x²)e-2x) at the point x=0 would be of the form y = mx + b, where m is the slope and b is the y-intercept.