At x= 1, x = 1, is f (x) f (x) concave up or concave down? Based on your answer above, is your estimate of f (1.001) f (1.001) too high or too low? Find the linear approximation of f (x)= sinx f (x) = ...

Formulate linear and integer programming problems for solving commonly encountered optimization problems. Understand how approximation algorithms compute solutions that are guaranteed to be within ...

Find the linear approximation of \ (f (x)=\sin x\) about the point \ (x=\pi /6\text {.}\) Explain why \ (f\) satisfies the conditions of the Mean Value Theorem.