MATHEMATICS · Multi-part · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
Let g(t)=tlnt for t>0. A table of calculator values gives g(2.1)≈0.3533.
(a) Find g′(t) in simplified form.
(b) Write the equation of the line tangent to the graph of g at t=2.
(c) Use the line from part (b) to approximate g(2.1). Show your calculation.
(d) Using the calculator value provided, compute the percent error of your approximation from part (c). State whether your approximation is an overestimate or an underestimate and explain your reasoning briefly.