The Calculus with Analytic Geometry |
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Page 273
... value on the interval . These intervals can be either closed , open , or closed at one end and open at the other . The greatest function value on an interval ... absolute minimum value of Section 3.1 273 MAXIMUM AND MINIMUM FUNCTION VALUES.
... value on the interval . These intervals can be either closed , open , or closed at one end and open at the other . The greatest function value on an interval ... absolute minimum value of Section 3.1 273 MAXIMUM AND MINIMUM FUNCTION VALUES.
Page 275
... absolute maximum value nor an absolute minimum value on [ 1,5 ] . See Fig . 3.1.12 for a sketch of the graph of f . lim f ( x ) = ∞ ; so x → 3- - f ( x ) can be made less than any negative number by taking 3 ... MINIMUM FUNCTION VALUES 275.
... absolute maximum value nor an absolute minimum value on [ 1,5 ] . See Fig . 3.1.12 for a sketch of the graph of f . lim f ( x ) = ∞ ; so x → 3- - f ( x ) can be made less than any negative number by taking 3 ... MINIMUM FUNCTION VALUES 275.
Page 334
... absolute minimum value is -√2 . There is no absolute maximum value of ƒ on ( 0 , + ∞ ) . For certain functions the following theorem is useful to determine if a relative extremum is an absolute extremum . Let the function ƒ be ...
... absolute minimum value is -√2 . There is no absolute maximum value of ƒ on ( 0 , + ∞ ) . For certain functions the following theorem is useful to determine if a relative extremum is an absolute extremum . Let the function ƒ be ...
Common terms and phrases
absolute minimum value angle antiderivative axis chain rule closed interval cos² cost function critical numbers curve decreasing defined by f(x definite integral derivative determine differentiable dollars domain of ƒ Draw a sketch EXAMPLE Exercises exists f(x₁ FIGURE Find an equation Find the volume formula ft/sec function defined function ƒ function values ƒ and g ƒ is continuous Given f(x graph is concave graph of ƒ horizontal ILLUSTRATION inequality L₁ L₂ length lim Ax-0 lim f(x Limit Theorem m₁ marginal cost marginal revenue maximum obtain open interval parabola point of inflection proof radius rate of change real numbers rectangle region bounded relative extremum relative minimum value Riemann sum Rolle's theorem satisfied sec² Section shown in Fig sin² slope solid of revolution SOLUTION square units tangent line total cost triangle value of ƒ vertical x₁ y₁ zero