SOLUTION: Find the open intervals where the function is concave up and concave down. f(x)= x^3 -3x^2 -1 Answer: concave up (1,infinity) concave down (-infinity, 1) i

Question 1100669: Find the open intervals where the function is concave up and concave down.
f(x)= x^3 -3x^2 -1
Answer: concave up (1,infinity)
concave down (-infinity, 1)
i dont understand because i got 0,2 for the critical points when you equal the whole derivative to zero. So please explain how to do it by hand without the calculator. Thanks.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
f(x)= x^3 -3x^2 -1
It's true that the first derivative shows critical points of 0, 2
The inflection point uses the second derivative, which is 6x-6
at 0, f''(x) is -6 and at (0.5) it is -3 and at 1 it is 0 and at 1.5 it is +3
Therefore, the concavity changes at 1. The critical points will be where there are local maxima or minima; the concavity changes are in between somewhere.
RELATED QUESTIONS
Determine where the graph of the function is concave up and concave down (if you need to... (answered by jsmallt9,RAY100)

Find the open intervals where the function is concave up and concave down. f(x)= x^3... (answered by Boreal)

determine where the given function is concave up and where it is concave down f(x)=... (answered by nyc_function)

why am I having trouble figuring out concave up and down determine where the graph of... (answered by stanbon)

For f(x) = (2x + 3)^2 , find intervals on which f is increasing and decreasing then, find (answered by CubeyThePenguin)

find the largest open interval at which function is concave up or concave down and find... (answered by stanbon)

Calculus Question Consider the function {{{ f(x)=3x^5-5x^3+3 }}}. Use the first... (answered by greenestamps)

For f(x) = x^2 - 7x + 10 , find intervals on which f is increasing and decreasing then,... (answered by Alan3354)

Where is the function, f(x)=(x^3)/(x^2 - 36) concave... (answered by ewatrrr)