15. Rates of Change, Area, and Volume
United States of America
Grades 9-12
15.05 The derivative as a limit
Interactive practice questions
Consider the function $f\left(x\right)=2x^2$f(x)=2x2
a
By filling in the table of values, complete the limiting chord process for $f\left(x\right)=2x^2$f(x)=2x2 at the point $x=1$x=1.
| $a$a | $b$b | $h=b-a$h=b−a | $\frac{f\left(b\right)-f\left(a\right)}{b-a}$f(b)−f(a)b−a |
|---|---|---|---|
| $1$1 | $2$2 | $1$1 | $\editable{}$ |
| $1$1 | $1.5$1.5 | $\editable{}$ | $\editable{}$ |
| $1$1 | $1.1$1.1 | $\editable{}$ | $\editable{}$ |
| $1$1 | $1.05$1.05 | $\editable{}$ | $\editable{}$ |
| $1$1 | $1.01$1.01 | $\editable{}$ | $\editable{}$ |
| $1$1 | $1.001$1.001 | $\editable{}$ | $\editable{}$ |
| $1$1 | $1.0001$1.0001 | $\editable{}$ | $\editable{}$ |
b
The instantaneous rate of change of $f\left(x\right)$f(x) at $x=1$x=1 is:
Easy
7min
Consider the function $f\left(x\right)=x^2$f(x)=x2
Easy
6min
Consider the function $f\left(x\right)=4^x$f(x)=4x
Easy
7min
Consider the function $f\left(x\right)=-x^2+5$f(x)=−x2+5
Medium
6min
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