Rolle's Theorem, Mean Value Theorem, and Optimization
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Test your skills and solve problems on Rolle's Theorem, the Mean Value Theorem, and Optimization! For: A.P. Calculus A.B. students
Topics of this game:
- f(x) continuous on [a,b] and differentiable on (a,b), f'(c) = (f(b)-f(a))/(b-a) Tangent slope equals secant slope on [a,b]
- Use M.V.T. for f(x) = (x+1)/x on [.5,2] f ' (x) = ? (Write Out Response)
- f(x) continuous on [a,b] and differentiable on (a,b), f(a) = f(b), proves that x = c exists where f'(c) = 0; relative extrema exists
- Does Rolle's Theorem apply for y = (x-3)(x+2)^2 on [-1,3]? Answer: Correct or Invalid
- Used to find absolute minimum or absolute maximum value of a function using derivatives
- Open box with surface area of 108 in.^2, find height dimensions for maximum volume (Write Out Response, Including Units)
- Does Rolle's Theorem apply for y = x-(x)^(1/3) on [0,1]? Answer: Correct or Invalid
- Use M.V.T. for f(x) = cos(x) on [0, pi/3] f ' (x) = ? (Round to Three Places After Decimal, Write Out Response)
- f(x) = (x^2) - 3x +2 on [1,2] By Rolle's Theorem, what are f(a) and f(b) equal to? (Write Out Response)
- Does Rolle's Theorem apply for f(x) = sin(2x) on [pi/6, pi/3]? Answer: Correct or Invalid
- Use M.V.T. for f(x) = (x^2) +1 on [-1,2] f ' (x) = ? (Write Out Response, Including Potential Negative Sign)
- Use M.V.T. for f(x) = (x^(2/3)) +1 on [1,8] x = ? (Round to Three Places After Decimal, Write Out Response)
- Determine point on curve y =x^2 closest to point (18,0) (Write Out Response)
- Find radius of right-circular cylinder of largest volume that can be inscribed in cone with r=6 in. and h=10 in. (Write Out Response, Including Unit)
- Can has volume of 1000 cm.^3, find radius of cylinder to minimize material r = [Blank] cm. (Round to Three Places After Decimal, Write Out Response)
