What is the first derivative test for critical points?
1 Answer
If the first derivative of the equation is positive at that point, then the function is increasing. If it is negative, the function is decreasing.
Explanation:
If the first derivative of the equation is positive at that point, then the function is increasing. If it is negative, the function is decreasing.
See Also:
http://mathworld.wolfram.com/FirstDerivativeTest.html
Suppose

If
#f^'(x)># 0 on an open interval extending left from#x_0 and f^'(x)<0# on an open interval extending right from#x_0# , then#f(x)# has a local maximum (possibly a global maximum) at#x_0# . 
If
#f^'(x)<0# on an open interval extending left from#x_0 and f^'(x)>0# on an open interval extending right from#x_0, then f(x)# has a local minimum (possibly a global minimum) at#x_0# . 
If
#f^'(x)# has the same sign on an open interval extending left from#x_0# and on an open interval extending right from#x_0, then f(x)# has an inflection point at#x_0# .
Weisstein, Eric W. "First Derivative Test." From MathWorldA Wolfram Web Resource. http://mathworld.wolfram.com/FirstDerivativeTest.html