Question

The function f (x) = 1 � x� � x5�is decreasing for​

Answer 1

Answer:

F(x)=1−x

3

−x

5

The critical point of F(x) are the values of x

for which either f

′

(x) does not exist or f

′

(x)=0

So f(x)=1−x

3

−x

5

f

′

(x)=−3x

2

−5x

4

f

′

(x)=0 when x=0

x=0 is the only critical point because 3+5x

2

>0

for all x∈R

f is decreasing on all the x value (x∈R)

because f

′

(x) < 0 for all x∈R