# The graph of the derivative of a function f x is

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Chapter P / Exercise 44
College Algebra
Redlin/Stewart
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2. The graph of the derivativeof a functionf(x) is given below.1234f’(a) What are the critical points off(x)?(b) Which critical point(s) correspond to relative extrema?(c) Can you determine any inflection points?(d) Graphf(x).3. Iff(x) =ax3+bx2+cx+d,find values for a,b,c, and d so thatf(x) hasa local maximum atx=-1, f(-1) = 2;f(x) has a local minimum atx= 1, f(1) =-135
ESP Math 408CWS#18Fall 19931. Givenax2+bx+c= 0, derive the quadratic formula.(Hint: you need tocomplete the square.)2. Prove that of all rectangles with given perimeterP, the square has thelargest area.3. Of all the triangles that pass through the point (2,1) and have two sideson the coordinate axes, find the dimensions of the one having the smallestarea.4.(a) Find the shortest line segment with endpoints on thexandyaxesgoing through the point (1,8).(b) What is the area of the triangle formed by the shortest line segment?(c) What is the rate of change of area with respect to thex-coordinateof the point on thex-axis?(d) For whichxis the area increasing?5. A garden is designed to be in the shape of a circular sector with radiusRand angleθ. If the areaAis to be a constant, find the dimensions (R, θ)which minimize the length of fence around the perimeter.6. A sector with angleφis cut from a circle of radius 12 inches, and theresulting edges are brought together to form a cone. Find the magnitudeofφso that the volume of the cone is maximum.7. Twenty feet of wire are to be used to form two figures.In each of thefollowing cases, how much should be used for each figure so that the totalenclosed area is a maximum?(a) equilateral triangle and square(b) square and regular pentagon(c) regular pentagon and hexagon(d) regular hexagon and circle(e) What can you conclude from this pattern?(Hint:The area of aregular polygon with n sides of length x isA= (n4)(cotπn)x2.)36
8. What are the dimensions of the lightest cylindrical aluminum can withcapacity 1,000cm3.9. Two hallways meet at right angles. Their widths areaandbas indicatedin the picture. What is the greatest length of a ladder which can be crriedhorizontally around the corner?

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The document you are viewing contains questions related to this textbook.
Chapter P / Exercise 44
College Algebra
Redlin/Stewart
Expert Verified