Answer: y = -4x + 4
Explanation:
use the product formula (ab' + a'b) to find the derivative:
x * (1 - 2x)³
a = x a' = 1
b = (1 - 2x)³ b' = 3(-2)(1 - 2x)²
= -6(1 - 2x)²
ab' + a'b
= x(-6)(1 - 2x)² + 1(x)
= -6x(1 - 2x)² + x
Plug in the given x-values to find the slope:
= -6(1)(1 - 2(1))² + (1)
= -6(-1)² + 1
= -6 + 1
= -5
Next, input the slope and the point into the Point-Slope formula:
y + 1 = -5(x - 1)
y + 1 = -4x + 5
y = -4x + 4