The slope of the tangent line is equivalent to the value of the derivative of the curve at the given point. derivative = 4x - 4y³ derivative at (1,1) = 4(1) - 4(1)³ derivative at (1,1) = 0
2 x² - y^4 = 1 y^4 = 2 x² - 1 y = (2x² - 1 )^(1/4) y = 1/4 · ( 2 x² - 1 )^(-3/4) · 4 x = = x / (2x² - 1 )^(3/4) m = y(1) = 1 / 1 = 1 m = 1 The equation of the tangent line: y - y1 = m ( x - x1) y - 1 = 1 · ( x - 1 ) Answer: The equation at the point ( 1, 1 ) is: y = x
