y = x^(2/3) * ((5/2)-(x)
y' = (2/3)x^(-1/3)*(5/2 - x) + x^(2/3)(-1)
= 5(1-x) / (3*x^(1/3))
So, y'=0 when x=1
y" = -5(2x+1) / (9x^(4/3))
y"(1) < 0, so f(1) is a maximum
See the graph at
http://www.wolframalpha.com/input/?i=+%28x^2%29^%281%2F3%29+*+%28%285%2F2%29-%28x%29
Hello. I have a few questions from my study guide, that I need to know to study for my test.
1) x^(2/3)*((5/2)-(x)
a) determine the ordered pairs of the local extrema of the function. Use the second derivative test.
B) determine the ordered pairs of all inflection points of the function.
2) Verify that the hypotheses for the Mean Value Theorem hold and find all the values of C that satisfy it's conclusion
F(x)= Cosx-Sin x [0,2pi)
1 answer