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- If xis large, which function grows faster, f(x)=2x or g(x)=x2?Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what x-values does the graph of ƒ have an inflection point?find the first derivative and solve it for x after setting it to zero. Substitute the x-values obtained as well as your endpoints into the original functions to observe the y-values. Only subs x-values that lie within the closed interval given.
- Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what x-values does the graph of ƒ have an inflection point?Suppose that the first derivative of y = ƒ(x) is y′ = 6x(x + 1)(x - 2). At what points, if any, does the graph of ƒ have a local maxi-mum, local minimum, or point of inflection?The second derivative of a function is equal to 1. If the graph of the function passes through (0,2) and (1,4), find f(2).