Consider the function g(x)=x2sec(3x)−4x defined for all x in a neighborhood of 0.2.
(a) Derive an explicit expression for g′(x).
(b) Evaluate g′(0.2), giving a numerical answer accurate to three decimal places.
(c) Using the tangent line at x=0.2, obtain a linear approximation (local linearization) L(x) for g(x) near x=0.2.
(d) Use L(x) to approximate g(0.25). Then discuss whether this approximation is likely an overestimate or an underestimate, supporting your conclusion with reasoning based on the concavity of g near x=0.2. No second derivative calculations are required, but your argument must reference appropriate calculus principles.