Post #18

Well, this past week in calculus was .. just two days. Monday we reviewed some more things that we did not understand throughout the year. I can honestly say that I am BEGINNING to understand the stuff that Mrs. Robinson taught us about the picture of a graph, so I think that’s what I’m going to explain.
• If you have f(x):
o Use a solid line to divide where it’s increasing or decreasing: if it’s increasing then the first derivative is positive, and if it’s decreasing then the first derivative is negative.
o Use a dotted line to separate concave up and concave down: if it’s concave up then the second derivative is positive, and if it’s concave down then the second derivative is negative.
o Put a large dot on MAX and MIN: MAXs and MINs mean that it’s a horizontal tangent and the first derivative is zero.
o Put an open circle on points of inflection: points of inflection is where the second derivative is zero.
• If you have f’(x):
o Use a solid line where it’s increasing or decreasing: if it’s increasing then the second derivative is positive, and if it’s decreasing then the second derivative is negative.
o Use a dotted line where it’s above and below the axis: when it’s above then the original is increasing and when it’s below then the original is decreasing.
o Use solid dots on MAX’s and MIN’s then the second derivative is equal to zero and it’s a point of inflection on the derivative.
o Then put open circles on the x intercepts: when the MAX is above the axis then it’s below for the second derivative, and when the MIN is below the axis then it’s above for the second derivative.
So I know that I understand the concept perfectly fine and it’s really simple, it’s just that looking at a graph confuses me so I would need more practice to look at the graph and figure out what is what. I didn’t do so well on my exam so it looks like I’ll be reviewing a lot over the break so I can catch up. THANK GOD IT’S THE HOLIDAYS.
~ElliE~