Consider the function f(x) = 5/4x^4 + 2/3x^3 - 5x^2 - 4x + 5

a. Find any relative extrema for f(x); be sure to label each as a maximum or minimum. You do not need to find function values; just find the x-values.

b. Determine the interval(s) where f(x) is increasing (if any) and the interval(s) where f(x) is decreasing (if any).

c. Determine the number of inflection points for this function and find their x-coordinate(s).

d. Determine whether f(x) is concave up or down at the following points: x = -2, x = -1, x = 0, and x = 2. Use this information and the information in parts A - C to sketch this function.

I really need help, and any help is greatly appreciated.

  1. 👍
  2. 👎
  3. 👁
  1. y = 5/4x^4 + 2/3x^3 - 5x^2 - 4x + 5
    y' = 5x^3 + 2x^2 - 10x - 4 = (5x+2)(x^2-2)
    y" = 15x^2 + 4x - 10

    a. extrema where y'=-
    max if y" < 0, min if y" > 0

    b. increasing where y' > 0

    c. inflection points where y" = 0

    d. concave up if y" > 0

    Now just plug in your numbers and functions.

    1. 👍
    2. 👎
  2. To check:

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. calc

    let f be function given by f(x)= Ln(x)/x for all x> 0. the dervative of f is given by f'(x)= (1 - Ln(x))/x squared. a) write equation for the line tangent to the graph of f at x=e squared b) Find the x-coordinate of the critical

  2. Functions - math

    The function f is such that f(x) = 2x + 3 for x ≥ 0. The function g is such that g(x)= ax^2 + b for x ≤ q, where a, b and q are constants. The function fg is such that fg(x)= 6x^2 − 21 for x ≤ q. i)Find the values of a

  3. Calculus

    The price-demand and cost functions for the production of microwaves are given as p=235−x40 and C(x)=14000+70x, where x is the number of microwaves that can be sold at a price of p dollars per unit and C(x) is the total cost (in

  4. calculus

    Find the inverse of the following function. Find the domain, range, and asymptotes of each function. Graph both functions on the same coordinate plane. f(x)=3+e^4−x

  1. College Algebra

    The graph of a quadratic function f(x) is shown above. It has a vertex at (-2,4) and passes the point (0,2). Find the quadratic function y=a(x-(-2))^2+4 y=a(x+2)+4 2=a(x+2)+4 -4 -4 -2=a(0+2)/2 -1+ a function -1(x+2)+4 ? Im not

  2. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4.

  3. math

    this question concerns the function f(x)=-2x3+3x2+12x+10 (a)find the stationary points of this function using the strategy to apply the first derivative test,classify the left hand stationary point found in part (a) find the

  4. inverse

    If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the inverse of this is x = cos(y) + 3 solve for y and you have your inverse The cos function only has a range of [-1,1], so the range of f(x) is [2,4]. this means

  1. MATH

    We now have d dx [x5 + y8] = 5x4 + 8y7y' = d dx [9] = 0. Rearranging this, we get 8y7y' = ?????????? ------------------------------------- A table of values for f, g, f ', and g' is given. x f(x) g(x) f '(x) g'(x) 1 3 2 4 6 2 1 8

  2. math

    The cost of producing q articles is given by the function C=f(q)=100+2q. (A) Find the formula for the inverse function. (B) Explain in practical terms what the inverse function tells you. I am pretty sure the answer to A is

  3. Calculus. I need help!

    Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer function y=f(u).] Then find the derivative dy/dx. y=√sinx √ is square root.

  4. Algebra 1 - Help!?

    Two big questions that are driving me mad. 1) Given the following linear function sketch the graph of the function and find the domain and range. f(x) = 2/7x - 2 2) Given the following linear function sketch the graph of the

You can view more similar questions or ask a new question.