Final answer:
The equation of the tangent line to the curve y = x^e - x^2 at the point (0,0) is found by taking the derivative and evaluating it at x=0, which results in a slope of 0. Thus, the tangent line is the horizontal line y = 0.
Step-by-step explanation:
To find an equation of the tangent line to the curve y = x^e - x^2 at the point (0,0), we need to calculate the derivative of the function to get the slope of the tangent at that point.
The derivative of y = x^e - x^2 is y' = e · x^(e-1) - 2x. Substituting the value x=0 into the derivative formula y' = e · 0^(e-1) - 2·0, we end up with y' = 0 since any nonzero term raised to the zero power is 1, and 0 multiplied by any factor is 0.
Thus, the slope of the tangent line at (0,0) is 0. The equation of a horizontal line passing through (0,0) is y = 0. Therefore, the equation of the tangent line to the curve at the point (0,0) is y = 0.