1. Let h(x) = x4 - 6x3 + 12x2. a. Find h'(x) and h"(x). 2. If f(x) = 6 ln(x), for x > 0, then: a. Find f '(x). b. Find f "(x). 3. Which function below has derivative F'(x) = 30x4 ? Hint: Differentiate each of the choices until you find a result that matches this F '(x). (A) F(x) = 120x3 (B) F(x) = 6x5 (C) F(x) = 120x5 (D) F(x) = 6x3 4. Let g(x) = x4 - 2x3 + 3/ x3 Find g'(x), given...
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...
Find the derivative of 6x3 - 2x + 1 f (2) [In other notation: f(x) = (6x^3 -2x +1) 7 x^(1/3)] (Simplify your answer as much as possible.) If your answer does not look like any of the four below, try choosing a number for x and plug it into your answer. Then plug that same number into each of the four answers to see which one matches. 1 1671 +- c 3 0 6x3 - 2x3 + x o...
Find the largest open interval on which the graph of the function f (x) = x4 +6x3 x is concave down Use interval notation, with no spaces in between numbers and brackets. For example: (3,8) Answer: Which of the following statements are true about the function below on the interval [a,b]? AA The derivative is 0 at two values of x both being local maxima. The derivative is 0 at two values of x, one on the interval [a,b] while...
5 4 3 + - + 6x - 4x + 8)e to Find the derivative of the function. y= (2x3 – 2x2 + 8x - 6)e ** O B. (6x5 - 6x4 + 24x3 – 12x2 - 4x + 8)e O C. (6x5 - 6x4 + 24x3 – 1872)e ** OD. (6x2 - 4x+8)e ** to
Let f be a twice differentiable function on an open interval (a, b). Which statements regarding the second derivative and concavity are true? If f"(c) is positive, then the graph of f has a local maximum at x = c. The concavity of a graph changes at an inflection point. If f is increasing, then the graph of f is concave down. The graph of f has a local minimum at x = c if f"(c) = 0. The graph of f is concave up if...
5. Given the function f(x)=x4 - 4x3 a) find f'(x) and the critical numbers of f. b) determine the interval(s) on which the graph off is increasing c) find f"(x) and the x-coordinates of the possible inflection points d) determine the interval(s) on which the graph off is concave down.
; Let at be a linear transformation as follows : T{x1,x2,x3,x4,x5} = {{x1-x3+2x2x5},{x2-x3+2x5},{x1+x2-2x3+x4+2x5},{2x2-2x3+x4+2x5}] a.) find the standard matrix representation A of T b.) find the basis of Col(A) c.) find a basis of Null(A) d.) is T 1-1? Is T onto?
. If not, explain why not. . x4 + 6x3 + 7.x2 – 6.– 8 27-4 3.x2 + 14.2 + 8 (e) lim- (f) lin e42 - 1 (f) lim sin(2.c) (g) lim sin?(36) x sin c (h) lim tan(5x) csc(4x) 0- 0
Find the derivative of the function. F(x) = (x4 + 3x2 - 2) F'(x) F(x) = Find the derivative of the function. f(x) = (3 + x)2/ f'(x) = Find the derivative of the function. g(t) = 7+4 + 4)5 g'(t) =