Find an equation for the tangent to the ellipse (x2/4) + y2 = 2 at the point (−2, 1).

Step 1: Write down the equation of the ellipse. The given equation is (x^2/4) + y^2 = 2.

Step 2: Differentiate the equation with respect to x to find the slope of the tangent line at any point (x, y) on the ellipse. The derivative is (x/2) + 2y*y' = 0.

Step 3: Solve the derivative equation for y', which gives the slope of the tangent line. y' = -x/(4y).

Step 4: Substitute the coordinates of the given point into the equation for y' to find the slope of the tangent line at that point. Substituting x = -2 and y = 1 gives y' = -(-2)/(4*1) = 1/2.

Step 5: Use the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point, to write the equation of the tangent line. Substituting m = 1/2, x1 = -2, and y1 = 1 gives y - 1 = 1/2(x + 2).

Step 6: Simplify the equation to put it in slope-intercept form, y = mx + b. The equation of the tangent line is y = 1/2x + 2.