Quick question regarding Analytical Applications of Differentiation

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The following quick question regarding: Analytical Applications of Differentiation

References:
https://teachingcalculus.com/2021/10/12/unit-5-analytical-applications-of-differentiation-2/
https://calculus.flippedmath.com/unit-5.html

Transcript:

The continuous function g, consisting of two line segments and a parabola, is defined on the closed interval [−3, 6], is shown. Let f be a function such that f(1) = 1/e  and f ′(x) = e^(−x) (1 − x).

Part A: Complete the table with positive, negative, or 0 to describe g′ and g″. Justify your answers. (3 points)

Table attached

Part B: Find the x-coordinate of any critical points of f and classify as a relative minimum, a relative maximum, or neither. Justify your answers. (3 points)

Part C: Find all values of x at which the graph of f has a point of inflection. Justify your answers. (2 points)

Part D: Let h be the function defined by h(x) = 2f(x)g(x). Is h increasing or decreasing at x = 1? Justify your answer. (2 points)

• Low bounty for a multiple part question.

• @blue can you please answer it, we don't turn things in near the deadline. Thanks

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