f(x) = 6 - x^2
Find the interval on which f is increasing and find the interval on which f is decreasing
Explain how you got it
Find the interval on which f is increasing and find the interval on which f is decreasing
Explain how you got it
-
f(x)=6-x^2
d/dx=-2x
-2x=0 when x=0.
you solve when x=0 because when the derivative is 0 it is a "critical point" or a "turning point" in the graph, meaning the slope changes sign.
when x<0,
the function is increasing because using the derivative, plugging a negative x yields a positive answer, thus it is increasing before 0,
when x>0,
the function is decreasing because again using the derivative, any positive x value yields a negative derivative, meaning slope is negative.
so, the function is increasing (-infinity,0) and decreasing (0,+infinity)
you must plug in values before and after when x=0 to determine whether the derivative is positive or negative. if you have more than just one critical point you must do it for all critical points.
d/dx=-2x
-2x=0 when x=0.
you solve when x=0 because when the derivative is 0 it is a "critical point" or a "turning point" in the graph, meaning the slope changes sign.
when x<0,
the function is increasing because using the derivative, plugging a negative x yields a positive answer, thus it is increasing before 0,
when x>0,
the function is decreasing because again using the derivative, any positive x value yields a negative derivative, meaning slope is negative.
so, the function is increasing (-infinity,0) and decreasing (0,+infinity)
you must plug in values before and after when x=0 to determine whether the derivative is positive or negative. if you have more than just one critical point you must do it for all critical points.