Question

Problem Zero: Read the section and make your own sum-

mary of the material.

Short answer

The combination of position function and direction is defined as velocity function.

The slope of any tangent line at any point $x=c$is defined as$f\text{'}\left(c\right)=\underset{h\to 0}{\lim }\frac{f(c+h)-f\left(c\right)}{h}.$

The line that passes through points $\left(a,f\left(a\right)\right)\&(b,f(b\left)\right)$on an interval $(a,b)$is known as the secant line.

The average rate of change becomes the instantaneous rate of change as$∆x\to 0.$

Step-by-step solution

Step 1. Given information.

The topic of the given section is An Intuitive Introduction to Derivatives.

Step 2. Summary of section.

The combination of position function and direction is defined as velocity function.

The slope of any tangent line at any point $x=c$is defined as $f\text{'}\left(c\right)=\underset{h\to 0}{\lim }\frac{f(c+h)-f\left(c\right)}{h}.$

The line that passes through points role="math" localid="1649811552168" $\left(a,f\left(a\right)\right)\&(b,f(b\left)\right)$on an interval $(a,b)$is known as the secant line.

The average rate of change becomes the instantaneous rate of change as role="math" localid="1649811585656" $∆x\to 0.$