To find critical points of f derive the function first and equates to zero
Apply the formula
To find critical points
Apply Sum and product of zeros
Common same terms out side
Common out side
Critical points are and
For Problem 1, find the exact values of the critical points of f. 1. f(x) =...
Find the inflection points of f(x)=x4+x3−3x2+8. Enter the exact answers in increasing order. x= x=
1. (12 points) Find all the critical points of f(x) = (x - 1)(x + 5) Hint: Do not expand! Instead use the product and chain rules then factor 2. (12 points) Find the absolute extrema of f(x) = on (-1,2). Give your answers as (x,y) points. Hint: It is much easier to take the derivative of f(x) by rewriting as f(x) = (1 + x4)-1 and use the chain rule 3. f(x) = ? - 7x + 1 (a)...
[6 points] Suppose that f'(x) = 3x2 + 2x + 7 and f(1) = 11. Find the function f(x). Of(x) = x3 + x2 + 7x + 11 Of(x) = x3 + x2 + 7x + 2 Of(x) = 6x + 5 Of(x) = x3 + x2 + 9 10. V MY NOTES [6 points] Find the integral: 15x3/2 + 21n|x[ + c 10 x3/2 + 2\n\xl + C O 5x1/2 - + c şx-1/2 - + c
5. Let f(x,y) = 3x2 y - y3 - 6x. (a) Find all the critical points off. (b) Classify each of the critical points; that is, what type are they? (c) For the same function f(x,y), find the maximum value of f on the unit square, 0 SX S1,0 <y s 1.
Find the values of x, y and z that correspond to the critical point of the function z = f(x,y) 3x2 + 5x + 5y + 2y?: = Enter your answer as a number (like 5, -3, 2.2) or as a calculation (like 5/3, 2^3, 5+4). T= Preview y= Preview z= Preview License Points possible: 10 Unlimited attempts.
2) For f(x) = (x? - 25W find f'(x) and the critical values of f. 3) For $(x) = 1 1 1 find f'(x) and the critical values of f. RI # .
Recall: For a function y = f(x), the critical points are (c,f(c)) for all c for which f,(c) = 0 Each such point is a relative maximum if f"(c) < 0 and a relative minimum if f"(c) > 0 For the following functions, find all critical points and determine if they are relative minimum or maximum, if possible. y-x2-4x 1 y=x3-6x2 + 9x-2 (4 У х Recall: For a function y-(x), the inflection points are (d.f(d)) for all c for...
URGENT 2) Find the x coordinates of all relative extreme points of f(x)÷4÷3 1 4.2.3.3,2+4 2+4 2) A) x--3,1 B)x=0 C)x=-3, 0, 1 D) x-1, 0.3 E) x-1.3 3) Find the x coordinates of all relative extreme points of fo) 4-33-6x2-1 ints of f(x)- 4- 3-6x2-1 3) A) x2, 0,3 B)x 0 C)x=-2.3 D) x--3,2 E) x--3,0,2 4) Find the relative minimum point(s) of fx)x35x2-10. 4) A) (0, f(o)) B) (-2, f(-2)) and (5, f(5)) C) (-2, f(-2)) and (0,...
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...
Problem #10: [2 marks] Find the two critical values of the function f(x) = x2/5 (6 – 3x). Problem #10: separate your answers with a comma