Answered

Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Get immediate and reliable answers to your questions from a community of experienced professionals on our platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

find the intervals from which f is increasing or decreasing for f(x)=3x^2/5-x^3/5

Sagot :

Hippalectryon
[tex]f(x)=3x^{2/5}-x^{3/5}[/tex]

We get the derivative : [tex]f'(x)=3*2/5*x^{2/5-1}-3/5*x^{3/5-1}=\dfrac{6}{5x^{3/5}}-\dfrac{3}{5x^{2/5}}[/tex]

f'(x) is negative for x<0.

Let's look at the critical points other than at x=0:
f'(x)=0 <=> 6/5-(3/5)x^(1/5)=0 <=> x^(1/5)=(6/5)*(5/3)=2 hence x=2^5=32

There is a critical point at x=32; for x<=32 f' is positive, for x>=30 f' is negative.

The derivative is positive for positive xs and negative for negative xs, hence f is increasing for 32>=x>0, and decreasing for x<0 and x>32
We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.