§1.8 The tangent line approximation (continued)

Exercises (continued)

Summary

A function $p$ has local linearization $L(x) = -2x + 5$ at $a = 3$. What are $p(3)$ and $p'(3)$?

Near $x = 3$, a shared tangent line $L$ approximates $f$ and $g$, where $f''(3) = 0.2$ and $g''(3) = -1$. Why does $L$ approximate $f$ better?

An object has position $s(9) = 4$ feet and velocity $s'(9) = -1.2$ feet per second at $t = 9$ seconds. The tangent line estimate of $s(9.34)$ is

A potato satisfies $F(30) = 167.6$ degrees and $F'(30) \approx 2.065$ degrees per minute. Use the tangent line at $30$ to estimate $F(33)$, rounded to three decimals.

With local linearization $L(x) = -2x + 5$ at $a = 3$, estimate $p(2.79)$, rounded to two decimals.

If $p''(x) \lt 0$ for $x \lt 3$ and $L$ is the linearization of $p$ at $3$, then $L(2.79)$ overestimates $p(2.79)$.