+ What are the hypercritical points for f(x) = x3 3x? ? (lf any exist at...
Consider the function f(x) = x3 + 3x² - 9x +1. (a) Identify all critical points of f(x). (Providing the -values will be sufficient. Hint: They will be integers.) (b) Use your answer from (a) to identify the absolute maximum value (global max) and absolute minimum value (global min) of f(x) over the x-interval (-2,2]. (Be clear and correct about what you are checking for full credit!)
Find, with justification, what the absolute maximum value of f(x) = x3 – 3x on the set of real numbers x satisfying x4 + 36 < 13x2. If time does not permit you to finish this question during the exam, please submit what you have and briefly explain what you would have tried.
Consider the following. f(x) = 1 4 x4 + 1 2 x3 − 3x2 + 4 Find f '(x). f '(x) = x3+ 3x2 2−6x Find f ''(x). f ''(x) = 3x2+3x−6 Find the x-values of the possible points of inflection. (Enter your answers as a comma-separated list.) x = Determine the intervals on which the function is concave up. (Enter your answer using interval notation.) Determine the intervals on which the function is concave down. (Enter your answer using...
The following exercises deal with the family of functions F(x) = x3 6. for λ > 0. a. Find all periodic points and classify them when 0< A<1. b. Prove that, if Ixl is sufficiently large, then lf"(x)| → oo. C. Prove that if λ is sufficiently large, then the set of points which do not tend to infinity is a Cantor set.
+ 1) Find all relative extrema for y = _ 13 x3 + 3x + 4 2) Find all absolute extrema of f(x) = 2x3 - 9x2 + 12x over the closed interval [ -3,3). Given: f(x) = 2x3 – 3x2 – 36x + 17 3) Find all critical values for f(x). 4) Find all relative extrema of f(x). 5) Find all points of inflection of f(x).
List all points (x,y) in the elliptic curve y2≡ x3 + 2x - 9 (mod
19). (Hint: Corresponding to any given x , points (x,y) and (x,-y)
can exist on the elliptic curve only if y2≡ x3 + 2x - 9 (mod 19) is
a quadratic residue mod 19. Recall that a value v
∊ Zp is a quadratic residue modulo p only if v(p-1)/2≡ 1 (mod p).
If v is indeed a quadratic residue, we can calculate the two...
QUESTION 3 x3 -4x2 +3x For what values of x is y undefined? Select all that apply -2 2 -1 üi -3
1) Graph the curve r(x) (x3-4x6-3xy for the values -2 3x K2 Find f(x) Determine unit tangent vector for x-1 Sketch unit tangent and unit normal vector for x-1
1) Graph the curve r(x) (x3-4x6-3xy for the values -2 3x K2 Find f(x) Determine unit tangent vector for x-1 Sketch unit tangent and unit normal vector for x-1
Multiple Choice: 1. Simplify "1-2x-x+5x-3x2+15+x3 a) x3-4x2+3x -1 (b) x2-4x2 +3x +1 (c) x3-4x-3x +1 (d)+4x +3x +1 2. Expand "logly' x3 a) 2(Logly)+3logx)) ( (d) 2logl)+3loglv) (b) 3log(x) 2logly) (c) 6log(x)logly) 3. quals 5 (b) 55 (c) 64 (d) 10 a) 62
sign Let f(x) 3x + 5, X, 2,2 - 3, X3-4,4 - 5, and Axu 1 mudy (m) Find (*)AX. radeb (b) The sum in part(a) approximates a definite integral using rectangles. The height of each rectangle is given by the value of the function at the left endpoint. Write the definite integral that the sum approximates. hapte (a) f(x)ax- Text 1 (Simplify your answer.)