Find the equation of the tangent line. y=(x^2+x-2)^2 at (-1,4)

Compute the derivative of y = (x² + x - 2)² using the chain rule:

dy/dx = 2 (x² + x - 2) d/dx [x² + x - 2]

dy/dx = 2 (x² + x - 2) (2x + 1)

Evaluate the derivative at x = -1 :

dy/dx (-1) = 2 ((-1)² + (-1) - 2) (2 (-1) + 1) = 4

This is the slope of the tangent line to the function at (-1, 4).

Use the point-slope formula to get the equation for the tangent line:

y - 4 = 4 (x - (-1))   →   y = 4x + 8

the correct answer is b. negative exponential growth.

step-by-step explanation:

you can tell it's an exponential function because it decreases rapidly then levels out and never touches the x-axis.

it is negative because the y-axis decreases as the x-axis increases.

therefore it is a negative exponential growth graph.

hope i !

step-by-step explanation: