Question

Suppose h(s)=\frac{1}{(s-8)^{2}} Find the largest value of A such that the function h(s) is increasing for all s in the interval (-\infty, A). A=

Answer 1

we differentiate

�

ff:

�

′

(

�

)

=

6

�

5

−

15

�

4

f

′

(x)=6x

5

−15x

4

f, prime, left parenthesis, x, right parenthesis, equals, 6, x, start superscript, 5, end superscript, minus, 15, x, start superscript, 4, end superscript [Show entire calculation]

Now we want to find the intervals where

�

′

f

′

f, prime is positive or negative.

�

′

(

�

)

=

3

�

4

(

2

�

−

5

)

f

′

(x)=3x

4

(2x−5)f, prime, left parenthesis, x, right parenthesis, equals, 3, x, start superscript, 4, end superscript, left parenthesis, 2, x, minus, 5, right parenthesis

�

′

f

′

f, prime intersects the

�

xx-axis when

�

=

0

x=0x, equals, 0 and

�

=

5

2

x=

2

5

​

x, equals, start fraction, 5, divided by, 2, end fraction, so its sign must be constant in each of the following intervals

Explanation: