(a) Find the interval(s) on which is increasing Recall the increasing/decreasing test with respect to a function f Therefore, the first step in finding the intervals of increase and decrease is to find f(x). x) sin(x) + 6 cos(x) ro) - 6 cos(x) - 6 sin(x) If f(x) > 0 on an interval, then fis increasing on that interval. • If F'(x) < 0 on an interval, then fis decreasing on that interval, YN Stap 2 We have determined that F(x)= cos(x)-6 sin(x). We must now determine any values where /(x)= 0. To do so, we set 6 cos(x)-6 sin(x) equal to 0 and solve for x over the interval 0sxs 2r. Doing so gives the following result. (Enter your answers as a comma-separated list.) 6 con(r)-6sin() We recall that these values are called the critical numbers off in the interval 0 5 x 5 2e. Sutet Sko (ou cannot come back) Sume Anwe

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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(a) Find the interval(s) on which is increasing.
Recall the increasing/decreasing test with respect to a function f
Therefore, the first step in finding the intervals of increase and decrease is to find f(x).
x) sin(x) + 6 cos(x)
ro) - 6 cos(x) - 6 sin(x)
If f(x) > 0 on an interval, then fis increasing on that interval.
If '(x) < 0 on an interval, then fis decreasing on that interval,
YN
Stap 1
We have determined that F'(x)=
cos(x)-6 sin(x). We must now determine any values where /(x)= 0. To do so, we set 6 cos(x)-6 sin(x) equal to 0 and solve for x over the interval
0sxs 2x. Doing so gives the following result. (Enter your answers as a comma-separated list.)
6com()-6sin(2)
We recall that these values are called the critical numbers off in the interval 0 5 x 5 2e.
Sutet Sko (rou cannot come back)
Sume Anwe
Transcribed Image Text:(a) Find the interval(s) on which is increasing. Recall the increasing/decreasing test with respect to a function f Therefore, the first step in finding the intervals of increase and decrease is to find f(x). x) sin(x) + 6 cos(x) ro) - 6 cos(x) - 6 sin(x) If f(x) > 0 on an interval, then fis increasing on that interval. If '(x) < 0 on an interval, then fis decreasing on that interval, YN Stap 1 We have determined that F'(x)= cos(x)-6 sin(x). We must now determine any values where /(x)= 0. To do so, we set 6 cos(x)-6 sin(x) equal to 0 and solve for x over the interval 0sxs 2x. Doing so gives the following result. (Enter your answers as a comma-separated list.) 6com()-6sin(2) We recall that these values are called the critical numbers off in the interval 0 5 x 5 2e. Sutet Sko (rou cannot come back) Sume Anwe
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