Derive a partial differential equation describing the evolution of the concentration b(x, t) of a population of bacteria along a water filament. assume that the bacteria reproduce locally at a rate proportional to their concentration, with proportionality constant λ, and that they diffuse with a flux proportional to −bx, with proportionality constant µ. in order to derive the equation, start with an integral principle describing

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Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.