Question

Value of the expression below on the horizontal span of 0 to 10. (Round your answer to two decimal places.)

x2 + 19x + 2

Answer 1

The value of expression increases from
`2` to
`292` on spanning
`x` from
`0` to
`10`.

Explanation:

The expression given here is

`x^2+19x+2`

Now if we differentiate this expression we can find the portions in its graph where it is increasing and decreasing or neither both.

If the differentiated expression is less than zero with the constant infront of highest degree positive then in the values corresponding to that
`x` the graph is decreasing.

If the differentiated expression is greater than zero with the constant infront of highest degree positive then in the values corresponding to that
`x` the graph is increasing.

`(d)/(dx)(x^2+19x+2)`

⇒
`2x+19`

For
`2x+19>0` ⇔
`x>(-19)/(2)`

For
`2x+19<0` ⇔
`x<(-19)/(2)`

Now for us the horizontal span is asked from 0 to 10 for the expression which is from
`x=0` to
`x=10` ,in which portion the value of the expression is strictly increasing so the vlaue increases from
`0+0+2=2` to
`10^2+190+2=292`.