SELECT PAGE NO.
No Books/Pages Are Available |
SELECT PROBLEM NO. FOR THE PAGE |
Graph the derivative function with the points:
Graph :
1. Draw the coordinate plane.
2. Plot the points.
3. Connect the points with a smooth curve.
Observe the derivative graph:
Critical points are the points where the curve touches the - axis.
The graph is increasing on since on .
The graph is again decreasing on since on .
Now draw the rough graph of .
(c)
changes from negative to positive at .
Therefore according to first derivative test , the function has minimum at .
changes from positive to negative at .
Therefore according to first derivative test , the function has maximum at .
(a)
(b) Critical points are and .
(c) has minimum at .
has maximum at .
"I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!" June Barnett |
"Your site is amazing! It helped me get through Algebra." Charles |
"My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful." Dan Pease |