Chapter 6: Q. 42 (page 419)

find the average rate of change of f from $0$ to $\frac{π}{6}$
$f (x) = s e c x$
.

Short Answer

Expert verified

the average rate of change of $f (x) = s e c x$ from $0$ to $\frac{π}{6}$ is $\frac{0.9}{π}$

Step by step solution

Step 1. Given data

The given function is

$f (x) = s e c x$

The given range is $[a, b] = [0, \frac{π}{6}]$

Step 2. average rate of change

The average rate of change f

$\frac{f (b) - f (a)}{b - a} = \frac{s e c (b) - s e c (a)}{b - a} = \frac{s e c (\frac{π}{6}) - s e c (0)}{\frac{π}{6} - 0} = \frac{1.15 - 1}{\frac{π}{6}} = \frac{6 (0.15)}{π} = \frac{0.9}{π}$

So average rate of change is $\frac{0.9}{π}$

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find the average rate of change of f from $0$ to $\frac{π}{6}$
$f (x) = s e c x$
.

Short Answer

Step by step solution

Step 1. Given data

Step 2. average rate of change

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find the average rate of change of f from 0toπ6f(x)=secx.

Short Answer

Step by step solution

Step 1. Given data

Step 2. average rate of change

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find the average rate of change of f from $0$ to $\frac{π}{6}$
$f (x) = s e c x$
.