Question

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 rewrote g(x) as x4 – 2x3 + 3 + C, for a constant C. Would this x3 change the derivative? 6. If f(x) = 6 ln(x), for x > 0, then: Find f '(x). a. b. Find f“(x). c. Use your answers for 6a-b to compute f(1), f '(1) and f“(1). 7. 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

Answer 1

4 @ h'w)= eine Gas - 6x2 +1242) 403 18x? + 24% h" (m) 12 x²_36x +24 h" (w) = 0 12(x-3x + 2) = 0 ~ 2, 2 : Concace Up in (-00, 1) Concave Down in Doernot freist © f'(x)= od man 6 6 1 <10 f" (m): 6 (%). 6. d ni dre 1) má f (o) = 6 Inci) = 0 FC07 ç = 6 f(1) = -6 oll 4+1 F'(x) = 30x4 5) ECH) F62-f201" du 30u 4+1 - sous bus Pls Rate positive :) 2 so Use quotient tale, g'(x) = 3d (124_24+3) - Ge? 2x373) da da le 3 (23)? (4x2 - 6x4)ne? 11 3x²(n4_2n²+3) 26 26 - 94² x4-9 NG x4 No