a) Let f(x) = −x^4 − 4x^3 . (i) Find the intervals of increase/decrease of f....

a) Let f(x) = −x^4 − 4x^3 . (i) Find the intervals of increase/decrease of f. (ii) Find the local extrema of f (values and locations). (iii) Determine the intervals of concavity. (iv) Find the location of the inflection points of f. (v) Sketch the graph of f. (You can choose your own scale for the graph)

b) A farmer wants to fence in an area of 6 km2 in a rectangular field and then divide it in half with a fence parallel to one of the sides of the rectangle. Find the dimensions of the rectangular field that minimize the amount of fence used.

Express the area of the region bounded by the graph of f(x) = 2 + √ x and the x-axis in the interval [3, 8] as a limit of sums using right endpoints. Do not evaluate the limit.

Expert Solution

milcah answered 2 years ago

Let f(x) = −x^4 − 4x^3. (i) Find the intervals of increase/decrease of f. (ii) Find...

Let f(x) = −x^4 − 4x^3. (i) Find the intervals of increase/decrease of f. (ii) Find the local extrema of f (values and locations). (iii) Determine the intervals of concavity. (iv) Find the location of the inflection points of f. (v) Sketch the graph of f. (You can choose your own scale for the graph)

1, Let f(x)=x^4-4x+10 Find the intervals of increase and decrease. A well labeled sign chart is...

1, Let f(x)=x^4-4x+10 Find the intervals of increase and decrease. A well labeled sign chart is usually enough here. 2, For the same function find relative extrema as ordered pairs. 3, For the same function find intervals of concavity (concave up/down) and any inflection points as ordered pairs.

Given f(x) = x^4 - 4x^3 1) find the intervals on which f is increasing or...

Given f(x) = x^4 - 4x^3 1) find the intervals on which f is increasing or decreasing. 2) find the local maximum and minimum values of f. 3) find the intervals of concavity and the inflection points

Find intervals of increase/decrease, max/min values, intervals of concavitiy. f(x)=x^3 -3x^2 +2

Let f(x)=(x^2)/(x-2) Find the following a) Intervals of increase/decrease (approximate the critical numbers to the nearest...

Let f(x)=(x^2)/(x-2) Find the following a) Intervals of increase/decrease (approximate the critical numbers to the nearest thousandths be sure to show the values tested) b) Local maxima and local minima c) Intervals of concavity and points of inflection (show all testing) d) Graph (x^2)/x-2 Label the intercepts,max/min, and inflection points. Indicate the window used on your calculator

part 1) Let f(x) = x^4 − 2x^2 + 3. Find the intervals of concavity of...

part 1) Let f(x) = x^4 − 2x^2 + 3. Find the intervals of concavity of f and determine its inflection point(s). part 2) Find the absolute extrema of f(x) = x^4 + 4x^3 − 8x^2 + 3 on [−1, 2].

Let f(x) = x^4 - 4x^3 - 18 x^2 + 77 a) a) Find all critical values of the...

Let f(x) = x^4 - 4x^3 - 18 x^2 + 77 a) a) Find all critical values of the function. [10] b) b) Find all intervals of increase and decrease. [10] c) Find all relative extrema. Use the second derivative test. Label each as a relative max. or a relative min. [10] d) d) Find on what interval(s) the function is concave up and concave down. [10] e) e) Find all inflection point(s), if any, of the function. [10]

f(x)=x^4-24x^2 Determine the intervals of increase and decrease for f (x) Use the First Derivative Test...

f(x)=x^4-24x^2 Determine the intervals of increase and decrease for f (x) Use the First Derivative Test to find all local maxima and minima for f (x) . Determine the intervals where f (x) is concave up and concave down Find any inflection points of f (x) . Please show the work

1. You are given the function f(x) = 3x^4 + 4x^3 a) Find the x and...

1. You are given the function f(x) = 3x^4 + 4x^3 a) Find the x and y- intercepts. b) Find the critical number(s) of f. c) Find the interval(s) of increase and decrease of f. d) Find the relative maximum and minimum value(s) of f. e) Find the hypercritical number(s) of f. f) Find the interval(s) of upward and downward concavity of f. g) Find the point(s) of inflection of f. h) Sketch the graph of f. 2. You are...

f(x)=e^x/(x+1) Find the vertical and horizontal asymptotes using limits. Also, intervals of increase and decrease, local...

f(x)=e^x/(x+1) Find the vertical and horizontal asymptotes using limits. Also, intervals of increase and decrease, local extrema. Finally, find the intervals of concavity and points of inflection.

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