Calculus Question

1.For the function 𝑓𝑓(𝑥𝑥)=4𝑥𝑥3+3𝑥𝑥26𝑥𝑥+1a) Find the intervals on which f is increasing or decreasing.

b)Find the x-coordinates of the local maxima and minima.

2.Discuss the concavity of the graph of 𝑦𝑦=𝑥𝑥−ln𝑥𝑥

3.Find all relative extrema of the function bellow. Use the Second Derivative Test.𝑔𝑔(𝑥𝑥)=2sin x +cos2𝑥𝑥 , (0,𝜋𝜋)

4.A farmer wants to fence an area of 6 million square feet in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. What should the lengths of the sides of the rectangular field be so as to minimize the cost of the fence?(Note: Make a labeled sketch and use Calculus to solve the problem.)

Powered by WordPress