Chapter 9.2, Problem 46E

To determine

To approximate the zeroes of f to the nearest tenth.

Answer to Problem 46E

The closest value is -0.2 and 5.6.

Explanation of Solution

Given information:

  $f(x)=-x^2+6x-2$

Calculation:

The given equation is $f(x)=-x^2+6x-2$

There are two intercepts: the one between 0 and 1, the 2^nd between 6 and 5.

Make a table between x - values between 0 and 1, 6 and 5. Use an increment of 0.1. Look for change of sign of the function values.

The table is

$x$	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9
$f(x)$	-1.41	-0.84	6.56	6.64	6.75	6.84	6.91	6.96	6.99

The change in sign is from 0.2.

$x$	5.1	5.2	5.3	5.4	5.5	5.6	5.7	5.8	5.9
$f(x)$	2.59	2.16	1.71	1.24	0.75	0.24	-0.29	-0.84	-1.41

The change in sign is from 0.2.

The function value that are closest to 0 correspond to x -values that best approximate the zeros of the function.

The closest value is -0.2 and 5.6.