\f2x For the function f(x) = X - 2 find f'"'(x), the third derivative of f, and f(4) (x), the fourth derivative of f. . . . 24 f''' ( x ) = - (x - 2)4 (( 4 ) ( x ) =Find any critical numbers for f and then use the second derivative test to decide whether the critical number(s) lead to relative maxima or relative minima. If f\"(c) = 0 or f\"(c) does not exist for a critical number c, then the second derivative test gives no information. In this case, use the rst derivative test instead. -x2+6x+29 f(x) What is/are the critical number(s)? Select the correct choice below and, if necessary, ll in the answer box to complete your choice. V The critical number(s) is/are x = 3 . (Simplify your answer. Use a comma to separate answers as needed.) There are no critical numbers. Where are the relative extrema? Select the correct choice below and, if necessary, ll in the answer box(es) to complete your choice. {-33 A- The function has a relative minimum at X: and a relative maximum at x = (Simplify your answers. Use a comma to separate answers as needed.) {-33 B- The function has a relative minimum at X: . There are no relative maxima. (Simplify your answer. Use a comma to separate answers as needed.) {-33 C. The function has a relative maximum at x= . There are no relative minima. (Simplify your answer. Use a comma to separate answers as needed.) {'21- D. There are no relative extrema. A study on optimizing revenue from a website considered dividing customers into two groups based on a value x between 0 and 1, where x measures the proportion of the total bandwidth requested by a customer. Customers with a request less than x were considered low revenue, and those above x high revenue. The expected revenue from the low revenue customers was described by the following function, where C and k are positive constants based on attributes of the website and the customers. Use the function to answer parts (a) and (b). R(x)=Cx(1e'k") (a) Find R'(x) and use it to find for what values ofx in [0,1] the revenue is increasing. What is R'(x)'? R'(x) = c + (ck)xe_ k" - ce' '0' For what values is the revenue increasing? Select the correct choice below and ll in the answer box to complete your choice. (Type your answer in interval notation.) A- The revenue is increasing where R(x) is positive. The revenue is increasing on B- The revenue is increasing where R'(x) is negative. The revenue is increasing on C. The revenue is increasing where R(x) is negative. The revenue is increasing on D- The revenue is increasing where R'(x) is positive. The revenue is increasing on Graph the function, considering the domain, critical points, symmetry, regions where the function is increasing or decreasing, inection points, regions where the function is concave upward or concave downward, intercepts where possible, and asymptotes where applicable. f(x)= 4x3 6x2 + 144x- 13 Choose the graph of the function. n_j:- A. B . .;: 600 y Q 00 y Q 600 y Q 4 o y Q X X x Q Q x Q Q 45 15 3o 30 45 15 [3. [3. 3o 30 [3. [3. 00 600 4 0 >600 Graph the function, considering the domain, critical points, symmetry, regions where the function is increasing or decreasing, inection points, regions where the function is concave upward or concave downward, intercepts where possible, and asymptotes where applicable. fG 48 (x) xX Choose the graph of the function. I: l_'l B_ I'V'I D_ q x> q x> Q x> q O 10 0 10 O 10 O 1 Complete parts (a) through (c) below for the given function. 2x f(x) = x2+9 (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. Find any intervals where the function is increasing. Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The function is increasing on the interval(s) (Type your answer in interval notation. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O B. The function is never increasing.Graph the function, considering the domain, critical points, symmetry, relative extrema, regions where the function is increasing or decreasing, inection points, regions where the function is concave upward or concave downward, intercepts where possible, and asymptotes where applicable. lnx f(x) = a Choose the correct graph below