Question

For fiddler crabs, the weight of the claw can be modeled as f(w) = 0.11w¹.54 pounds when the weight of the body is w pounds.€ note that f(w) is increasing and concave up for all w > 0. For positive values of w, will a linearization of f overestimate or underestimate the function values? Explain.

Answer 1

The linearization of f(w) will underestimate the weight of the claw for positive values of w.

Step-by-step explanation:

The linearization of a function is an approximation of the function using a linear function. In this case, the function is f(w) = 0.11w¹.54. Since f(w) is increasing and concave up for all w > 0, we know that the curvature of the function is positive. A linear approximation will always be a straight line with no curvature, so it will underestimate the function values when w is positive. This means that the linearization of f(w) will underestimate the weight of the claw for positive values of w.