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$$\frac{d^2y}{dx^2} = -\frac{(d - a)\,u\,(1 - u)}{b^2\,(1 + u)^3}$$

Usage

d2x_logistic4(x, a, b, c, d)

Arguments

x

Numeric vector. Independent variable (typically log10-concentration).

a

Numeric scalar. Lower asymptote (baseline response).

b

Numeric scalar. Scale parameter (\(b > 0\)); controls steepness.

c

Numeric scalar. Inflection-point location on the x-axis.

d

Numeric scalar. Upper asymptote (saturation response).

Value

Numeric vector of d²y/dx² values.