Question

In: Math

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]

Solutions

Expert Solution


Related Solutions

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...
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)
3. Let X = {1, 2, 3, 4}. Let F be the set of all functions...
3. Let X = {1, 2, 3, 4}. Let F be the set of all functions from X to X. For any relation R on X, define a relation S on F by: for all f, g ∈ F, f S g if and only if there exists x ∈ X so that f(x)Rg(x). For each of the following statements, prove or disprove the statement. (a) For all relations R on X, if R is reflexive then S is reflexive....
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
Using extended euclidean algorithm find f(x) and g(x) in: f(x)(x^5 + 4x^4 + 6x^3 + x^2...
Using extended euclidean algorithm find f(x) and g(x) in: f(x)(x^5 + 4x^4 + 6x^3 + x^2 + 4x + 6) + g(x)(x^5 + 5x^4 + 10x^3 + x^2 + 5x + 10) = x^3+1
Given f''(x)= 4x-6 and f'(-2)=5 and f(-2)=1 FIND: Find f'(x)= and find f(2)=
Given f''(x)= 4x-6 and f'(-2)=5 and f(-2)=1 FIND: Find f'(x)= and find f(2)=
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...
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded to 2 decimal places. f '(3)= 3....
2. Let f(x)=2x^2−4x+7/5x^2+5x−9, evaluate f '(x) at x=3 rounded to 2 decimal places. f '(3)= 3. Let f(x)=(x^3+4x+2)(160−5x) find f ′(x). f '(x)= 4. Find the derivative of the function f(x)=√x−5/x^4 f '(x)= 5. Find the derivative of the function f(x)=2x−5/3x−3 f '(x)= 6. Find the derivative of the function g(x)=(x^4−5x^2+5x+4)(x^3−4x^2−1). You do not have to simplify your answer. g '(x)= 7. Let f(x)=(−x^2+x+3)^5 a. Find the derivative. f '(x)= b. Find f '(3)= 8. Let f(x)=(x^2−x+4)^3 a. Find the...
Integral x^5-x^4+4x^3-4x^2+8x-4 / ( x^3+2)^3(x^2-1) dx
Integral x^5-x^4+4x^3-4x^2+8x-4 / ( x^3+2)^3(x^2-1) dx
Find the absolute maximum and minimum values of the function f(x, y) = x^2 + ((4/3)...
Find the absolute maximum and minimum values of the function f(x, y) = x^2 + ((4/3) y^3) − 1 on the disk x^2 + y^2 ≤ 1.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT