Suppose that the first and second derivatives of a function y=f(x) are given by: f'(x) = xe^x and f"(x) = e^x (x+1). Which of the following statements is true? a) f'(-1) > 0 b) f(x) is increasing and opens up (0, infinity) c) There are no critical points and there is one inflection point. d) f(x) is increasing and opens down on (negative infinity, -1) e) There are is one critical point and there are two inflection points. f) f"(x) > 0 on (negative infinity, -1) g) There are no critical points and there are two inflection points. h) f'(x) > 0 on (negative infinity, 0) i) f'(x) < 0 on (0, infinity) j) f"(x) < 0 on (-1, infinity)
Suppose that the first and second derivatives of a function y=f(x) are given by: f'(x) = xe^x and f"(x) = e^x (x+1). Which of the following statements is true? a) f'(-1) > 0 b) f(x) is increasing and opens up (0, infinity) c) There are no critical points and there is one inflection point. d) f(x) is increasing and opens down on (negative infinity, -1) e) There are is one critical point and there are two inflection points. f) f"(x) > 0 on (negative infinity, -1) g) There are no critical points and there are two inflection points. h) f'(x) > 0 on (negative infinity, 0) i) f'(x) < 0 on (0, infinity) j) f"(x) < 0 on (-1, infinity)
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From the graph below, observe any critical number(s), and describe corresponding slope(s) of the function.
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