Exam 14: Curve Sketching

Find the vertical asymptotes and non-vertical asymptotes of the following function.Do not sketch its graph. y =

Determine the intervals on which the function is increasing and on which it is decreasing.Also determine the points of relative maxima and relative minima. y = + - 3x + 7

Given y = f(x)= 4 - 4x + 5 on the interval ,find the values of x at which absolute maxima and absolute minima occur.

The cost equation for a cookie store is given by C(x)= - 6 + 250,where x is the number of cookies made (in dozens),and C(x)is the cost in dollars.Determine where the graph of the equation is concave up and where it is concave down and find any inflection points.

The graph of a function is given.Find (a)the open intervals on which the function is increasing or decreasing; (b)the coordinates of all relative extrema.

Let f(x)= .Determine the intervals of which f is (a)concave up and (b)concave down.(c)Find the x-values of all inflection points.

Find all the critical values of y = - - x + 2.

The graph of a function is given.Find (a)the open intervals on which the function is increasing or decreasing; (b)the coordinates of all relative extrema.

The cost equation for a hot dog stand is given by C(x)= 2 - 21 + 60x + 500,where x is the number of hot dogs sold,and C(x)is the cost in dollars.Determine where the graph of the equation is concave up and where it is concave down and find any inflection points.

Use your graphing calculator to find the absolute extrema of f(x)= - 4 + 3x + 2 on (round answers to 3 decimal places).

Sketch the graph of y = - 3 + x + 1 with the aid of intercepts,symmetry,and the first-derivative test.Use your graphing calculator to verify your solution.

If f(x)= ,determine the intervals on which f is increasing and the intervals on which f is decreasing.

The function f(x)= is concave up on the interval(s)

It is estimated that under a short-term energy-assistance plan,n million households will receive direct aid in meeting home-fuel costs after t years,where n = 2 - 15 + 36t,0 ≤ t ≤ 3.For what value of t will n be a maximum?

The profit equation for a taco stand is given by P(x)= -0.4 + 100x -100,where x is the number of tacos sold,and P(x)is the profit in dollars.Determine where the graph of the equation is concave up and where it is concave down and find any inflection points.

The function y = - 8 Has a relative maximum when x =

If f(x)= 7 + 3x - 2,determine the intervals on which f is increasing and the intervals on which f is decreasing.

Suppose that the total number of units produced by a worker in t hours of an 8-hour shift can be modeled by the production function P(t)= 4t + 24 - 2 .Find where the function is concave up and where the function is concave down.

An open box is to have a surface area of 300 .The base of the box is to be a square.Find the dimensions of the box that maximize volume.

If f(x)= ,determine the intervals on which f is increasing and the intervals on which f is decreasing.