Calculus Drill 111809 b A point moves along
Calculus Drill 11/18/09 b. A point moves along the curve y = √x in such a way that the yvalue is increasing at a rate of 2 units per second. At what rate is the x value changing for the following: b(a)x = 0. 5 (b) x = 1 (c) X = 4
Calculus Objective b. STW find extrema on an interval
Key Terms b. Minimum b. Maximum b. Extreme Theorem Value
Key Terms b. Critical Numbers b. Absolute Min/Max b. Relative Min/Max
Min/Max b. On an open interval b. On a closed Interval b. Not at all!
Extreme Value THRM b. IF ƒ is continuos on a closed interval than it has both a min and a max
Lets take a look! b. Y = b. Do 2 x + 2 (–∞, ∞) you have a max or min?
Lets take a look! b. Y = b. Do 2 x + 2 (–∞, ∞) you have a max or min?
Lets take a look! b. Y = b. How 2 x + 2 (–∞, ∞) about on the interval (– 3 , 3)
Lets take a look! b. Y = b. How 2 x + 2 (–∞, ∞) about on the interval (– 3 , 3)
Lets take a look! b. Y = b. How 2 x + 2 (–∞, ∞) about on the interval [– 3 , 3]
Lets take a look! b. Y = b. How 2 x + 2 (–∞, ∞) about on the interval (– 3 , 3)
Let’s Take a look! bƒ(x) = 3 x – 3 x (– ∞, ∞) b. Where do the min and max occur?
Let’s Take a look! bƒ(x) = 3 x – 3 x (– ∞, ∞) b. What is the slope at those points?
Critical Numbers b. Find the derivative and set it equal to zero.
b 1. What are critical points? b 2. When do absolute max/min and relative max/min occur
Critical Numbers b. Find the derivative and set it equal to zero.
Extrema b. Absolute Min/Max • Occurs on a closed interval
Extrema b. Relative Min/Max • Occurs on a open interval
Practice problems b. P 161 # 7– 14 , 19, 20
- Slides: 20