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 any other value of x.
1. Let h(x) = x4 - 6x3 + 12x2. a. Find h'(x) and h"(x). 2. If f(x) =...
a. 4. Let h(x) = x4 – 6x3 + 12x2. Find h'(x) and h"(x). b. Find the open intervals on which h is concave upward and concave downward. Give the points of inflection for h as ordered pairs. c. a. 5. Let g(x) = x4 – 2x3 + 3. x3 This function is defined, differentiable, for all real numbers except x = where g has a vertical asymptote. b. Find g'(x), given any other value of x. c. Suppose we...
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 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) =
3. (a) Write a MatLab program that calculates for the function F(x, y) = ln(x + Va,2-y2) The program should use pretty) to display both the original function and the differentiated result, and also use fprintf() to print a label such as "F(x,y) -" and "dF/dxdy - " in front of both the function and the derivative. Then have your program also print out the derivative again after it uses simplify() on the result (b) Find the Taylor expansion of...
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...
17. MULTIPLE CHOICE Let f(x) = x4 - 3x3 + 5x - 3. Use synthetic substitution to find f(-2). F 37 H -21 G 27 I -33 Given a polynomial and one of its factors, find the remaining factors of the polynomial. 18. 2x3 + 15x2 + 22x – 15; x + 5 19. 23 - 4x2 + 10x - 12; x - 2
Let f(x) = 2x2 - 12x2 - 30x-2. a. Find all points on the graph of f(x) at which the tangent line is horizontal. b. Find all points on the graph of f(x) at which the tangent line has slope 42. a. The tangent line is horizontal at the point(s) ; (Type an ordered pair. Use a comma to separate answers as needed.) b. The slope of the tangent line is 42 at the points) (Type an ordered pair. Use...
Differentiate. Let f and g be functions that satisfy: f(4)-1, g(4)--3, f'(4)--2,and g'(4)-3. Finod h(4) for h(x)-f(x)g(x)-2/(x)+'7 O-5 -13 13 Differentiate. Let f and g be functions that satisfy: f(4)-1, g(4)--3, f'(4)--2,and g'(4)-3. Finod h(4) for h(x)-f(x)g(x)-2/(x)+'7 O-5 -13 13
# 2,3,4,7, 10,11,15,18) Differentiate the function: #2 f(x) = ln(22 + 1) #3 f@) = ln(cos) #4 f(x) = cos(In x) #7 f(x) = log2(1 – 3x) #10 f(t) = 1+Int #11 F(x) = In( 3+1") #18 y = (ln(1 + e*)] # 23) Find an equation of the tangent line to the curve y = In(x2 – 3) at the point (2,0). # 27, 31) Use the logarithmic differentiation to find the derivative of the function. # 27 y...
Q4 (4 points) (a) (1.5p) Find f +g-h, fog, fog•h if f(x) = (x - 3, g(x) = x^, and h(x) = x* + 2 (b) 0(1p) Find the inverse of the function f(x) = 4x - 1 2x + 3 () (0.5p) Find f(-)) (c) Simplify: 0 (1p) In(a) + { ln(b) + Inc mais)