MATH 1009 Lecture 18: CH5-50-Functions of Several Variables

Sketch the graph of a function that satisfies:

𝑓(−3) = 2;𝑓(−1) = −5;𝑓(2) = −4; 𝑓(6) = −1

𝑓′(−3) = 𝑓′(6) = 0

lim 𝑥→0− 𝑓(𝑥) = −∞; lim 𝑥→0+ 𝑓(𝑥) = ∞

𝑓′′(𝑥) > 0 𝑖𝑓 𝑥 < −3 𝑜𝑟 0 < 𝑥 < 4

𝑓′′(𝑥) < 0 𝑖𝑓 − 3 < 𝑥 < 0 𝑜𝑟 4 < 𝑥

This is a question of Partial Differentiation