Get the derivative:
y = (9 - x²)¹ʹ³
dy/dx = 1/3 (9 - x²)⁻²ʹ³ d/dx [9 - x²]
dy/dx = 1/3 (9 - x²)⁻²ʹ³ (-2x)
dy/dx = -2/3 x (9 - x²)⁻²ʹ³
Evaluate it at x = 1 :
dy/dx (1) = -2/3 • 8⁻²ʹ³
Since 8 = 2³, we have
8⁻²ʹ³ = 1 / 8²ʹ³ = 1 / (2³)²ʹ³ = 1 / 2² = 1/4
Then the tangent line has equation
y - 2 = 1/4 (x - 1) → y = 1/4 x + 7/4
