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Published byIsaac Bartlett Modified over 2 years ago

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Let f be defined on an interval, and let x1 and x2 denote points in that interval. (a)f is increasing on the interval if f(x1)

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Use the graph of the equation y=f(x) in the accompanying figure to find the signs of dy/dx and dy/dx and d 2 y/dx 2 at the points A,B, and C. dy/dx 0 dy/dx >0, d 2 y/dx 2 <0 dy/dx<0, d 2 y/dx 2 <0

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Use the graph of f shown in the figure to estimate all values of x at which f has(a) relative minima, (b) relative maxima, and (c) inflection points 2B2Because the curve is turning negative to positive. 0 Because the curve is turning positive to negative 3 Because the slope of f is changing negative to positive

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Find any critical numbers of the function g(x) = x2(x2 - 6) g (x) = (x2) (x2 - 6) + (x2)(x2 - 6) g (x) = 2x(x2 - 6) + (x2)(2x) g (x) = 4x3 - 12x. g (x) = 4x(x2 - 3). Remember that a critical number is a number in the domain of g where the derivative is either 0 or undefined. Since g (x) is a polynomial, it is defined everywhere. The only numbers we need to find are the numbers where the derivative is equal to 0, so we solve the equation 4x(x2 - 3) = 0. The solutions are These are the only critical numbers.

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