Calculus - Functions?

#1. A cubic polynomial function f is defined by f(x) = 4x^3 +ax^2 + bx + k
where a, b and k are constants. The function f has a local minimum at x = -1, and the graph of f has a point of inflection at x= -2

a.) Find the values of a and b

#2. Let h be a function defined for all x (not equal to) 0, such that h(4) = -3 and the derivative of h is given by h'(x) = (x^2 - 2) / (x) for all x (not equal to) 0.

a.) Find all values of x for which the graph of h has a horizontal tangent, and determine whether h has a local maximum, a local minimum, or neither at each of these values. Justify your answers.

b.) On what intervals, if any, is the graph of h concave up? Justify

c.) Write an equation for the line tangent to the graph of h at x=4

d.) Does the line tangent to the graph of h at x = 4 lie above or below the graph of h for x > 4 ? Why?

  1. 👍 1
  2. 👎 0
  3. 👁 1,821
  1. I will do #1 for you.

    Show some work or steps that you have done for #2 and#4 and I will evaluate your work.

    #1:

    f '(x) = 12x^2 + 2ax + b
    f ''(x) = 24x + 2a

    f '(-1) = 0 = 12 - 2a +b ---> 2a - b = 12
    f ''(-2) = 0 = -48 + 2a ----> a= 24
    then 2(24) - b = 12
    b = 36

    a = 24 , b = 36

    1. 👍 4
    2. 👎 1
  2. a billion

    1. 👍 2
    2. 👎 3

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    An OPEN box has a square base and a volume of 108 cubic inches and is constructed from a tin sheet. Find the dimensions of the box, assuming a minimum amount of material is used in it's construction. HINT: the goal is to minimize

  2. Precalculus

    If p(x) is a cubic polynomial such that p(0) = 0, P(2) = -4 and P(x) is positive only when x > 4 find p(x).

  3. Maths

    true/false 1. a cubic polynomial has at least one zero.............. 2. a quadratic polynomial an have at most two zeroes.......... 3. if r(x)is the remainder and p(x) is the divisor, then degree r(x) < degree p(x)............ 4.

  4. calculus

    1.is the function f(X)=4-7x^5 a polynomial function? if so state its degree and leading coefficient. 6.use the remainder theorem to determine if x-2 is a factor of the polynomial f(x)=3x^5-7x^3-11x^2+2

  1. Math

    Which of the following statements about a polynomial function is false? 1) A polynomial function of degree n has at most n turning points. 2) A polynomial function of degree n may have up to n distinct zeros. 3) A polynomial

  2. algebra

    Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms. 2 – 11x^2 – 8x + 6x^2 A. –5x^2 – 8x + 2; quadratic trinomial B. –5x^2 – 8x; quadratic binomial C. –6x^2 – 8x

  3. POLYNOMIALS

    The cubic polynomial f(x) is such that the coefficient of x^3 is -1. and the roots of the equation f(x) = 0 are 1, 2 and k. Given that f(x)has a remainder of 8 when divided by (x-3), find the value of k. okay, this is what i did:

  4. Calculus

    A cubic polynomial function f is defined by f(x) = 4x^3 + ax^2 + bx + k? A cubic polynomial function f is defined by: f(x) = 4x^3 + ax^2 + bx + k where a, b, and k are constants. The function f has a local minimum at x= -1, and

  1. math

    Using only​ algebra, find a cubic function with the given zeros. -2, 3, -7 the polynomial function is: f(x)=x^3+ (BLANK) x^2-13x-42 i can't figure out what BLANK is Thank you!

  2. Calculus

    A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a. 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a.

  3. Math

    What does the degree of a polynomial expression tell you about its related polynomial function? Explain your thinking. Give an example of a polynomial expression of degree three. Provide information regarding the graph and zeros

  4. Polynomial Functions

    What do polynomial functions look like? And what can be consider a polynomial function? Would a graph that is like an upside down V be considered as a graph of a polynomial function?

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