Tina S.

# help needed with calculus question

The graph of the continuous function g is shown above for −3≤x≤5 . The function g is twice differentiable except at x=1

Graph:

http://prnt.sc/wdcalq

Let f be the function with f(1)=3 and derivative given by f′(x)=(6x^2−5x)e^x.

(a) Find the x -coordinate of each critical point of f . Classify each critical point as the location of a relative minimum, a relative maximum, or neither. Justify your answers.

(b) Find all values of x at which the graph of f has a point of inflection. Give reasons for your answers.

(c) Fill in the missing entries in the table below to describe the behavior of g′ and g′′ on the interval −3≤x≤5. Indicate Positive or Negative. Give reasons for your answers.

Chart: https://prnt.sc/wdcflj

(d) Let h be the function defined by h(x)=f(x)g(x) . Is h increasing or decreasing on the interval 1< x < 5? Give a reason for your answer.

Thank you

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