Posted by Cynthia on Tuesday, October 30, 2012 at 11:51pm.
1. Locate the absolute extrema of the function f(x)=cos(pi*x) on the closed interval [0,1/2].
2. Determine whether Rolle's Theorem applied to the function f(x)=x^2+6x+8 on the closed interval[4,2]. If Rolle's Theorem can be applied, find all values of c in the open interval (4,2) such that f'(c)=0.
3. Determine whether the open intervals on which the graph of f(x)=7x+7cosx is concave upward or downward.
4. Find the points of inflection and discuss the concavity of the function f(x)=sinxcosx on the interval (0,2pi)
5.Find the points of inflection and discuss the concavity of the function f(x)=x^3+x^26x5

Calculus  Steve, Wednesday, October 31, 2012 at 10:38am
1.
f' = pi sin(pi*x) extrema where f' = 0, or x an integer
2.
since f(x) = (x+4)(x+2) f(4)=f(2)=0, so we're good to do. vertex is at x = 3.
3.
f is concave up if f'' > 0
f'' = 7cosx, so where is that >0? <0?
4.
concavity as above, inflection where f'' = 0
f'' = sinx + cosx = √2 sin(x + π/4)
5.
same methods as in #3,4/
f'' = 6x
Answer This Question
Related Questions
 Calculus  Determine whether Rolle's Theorem can be applied to f on the closed ...
 Math  Determine whether Rolle's Theorem can be applied to f on the closed ...
 calculus  Determine whether Rolle's Theorem can be applied to f on the closed ...
 Calculus  1. Determine whether Rolle's Theorem applied to the function f(x)=((x...
 calc  Verify that the function satisfies the three hypotheses of Rolle's ...
 calc  Verify that the function satisfies the three hypotheses of Rolle's ...
 calculus  Rolle's theorem cannot be applied to the function f(x) = x1/3 on the ...
 calculus  Show that the function f(x)=4x^3−15x^2+9x+8 satisfies the three...
 URGENT!! PLEASE Calc  Verify that the function satisfies the three hypotheses ...
 calculus  determine whether the mean value theorem can be applied to f on the ...
More Related Questions