# 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. 👍
2. 👎
3. 👁
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. 👍
2. 👎
2. a billion

1. 👍
2. 👎
3. sus

1. 👍
2. 👎

## Similar Questions

1. ### pre-calc

1. which of the following is a fourth degree polynomial function? select all that apply. a. f(x)= 4x^3 - x^2 + 2x - 7 b. f(x)= 5-x^4 c. f(x)= 1 / 2x^4 + x^2 -5 d. f(x)= 3x^4 + 2x^3 -4x +1 2. which function below has the end

2. ### 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

3. ### 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

4. ### 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

1. ### 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

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. ### 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.

4. ### Pre-Calc

Fill in the blank; •In the process of polynomial division (Divisor)(Quotient)+_______=_______ •When a polynomial function f is divided by x-c, the remainder is _______. •If a function f, whose domain is all real numbers, is

1. ### CALCULUS DERIVATIVES CONTINUITY

Let f be the function defined by the piecewise function: f(x) = x^3 for x less than or equal to 0 x for x greater than 0 Which of the following is true? a) f is an odd function b) f is discontinuous at x=0 c) f has a relative