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Unformatted text preview: If graph f(x) is bounded by m&M m ≤ f(x) ≤ M (def integral lies between m(b-a) and M(b-a) ∆ t=(b-a)/n F Inc Dec CU CD Linear Horiz F’ +-Inc Dec Horiz X-axis (0) If a=b, then the integral will be zero since in that case, there will be no area under the curve. If I run 5 miles to the park and 5 miles home, then the total distance traveled is 10 miles (= total area under the curve) but my distance from my starting point is 0 miles(= integral) Step 1- Draw a pic & label at most two variables Step 2- Express the quantity you want to maximize or minimize in terms of your variables V=3x^2h Step 3- Constraint 10=3x^2+8 h x. Solve for one variable in terms of the other Step 4- Substitute- DON’T PLUG IN UNTIL HAVE THE FINAL FORMULA Find distance accurate within 20 ft: L − R = (v(0) − v(8))∆t = 80∆t 80∆t=20 ∆t=.25 sec...
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- Fall '09
- Derivative, def integral lies, Dec Horiz X-axis, Dec CU CD, degrees Continuous exponential