Thanks kindly **Exercise: Identify Absolute and Local Extrema****Instructions:**Sketch the graph of the function \( f \) and use your sketch to find the absolute and local maximum and minimum values of \( f \). Provide your answers in a comma-separated list. If an answer does not exist, enter "DNE."**Function:**\[ f(x) = 9 - \sqrt{x} \]**Questions:**- **Absolute Maximum Value:** [Enter your answer here]- **Absolute Minimum Value:** [Enter your answer here]- **Local Maximum Value(s):** [Enter your answer here]- **Local Minimum Value(s):** [Enter your answer here] **Verify that the function satisfies the three hypotheses of Rolle's theorem on the given interval. Then find all numbers \( c \) that satisfy the conclusion of Rolle's theorem. (Enter your answers as a comma-separated list.)**\[ f(x) = 3x^2 - 6x + 8, \quad [-1, 3] \]\[ c = \text{\_\_\_\_\_\_\_\_\_\_\_\_} \]

Note:- Since you have asked multiple question As per our policy, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question. Given Function:- fx=9-xHere parent function is gx=x ⇒fx=9-x So graph reflected over x axis and shift 9 units upward At x=0 ⇒f0=9-0=9 At x=1 ⇒f1=9-1=8 At x=4 ⇒f4=9-4=7 At x=9 ⇒f9=9-9=6 At x=36 ⇒f36=9-36=3 At x=81 ⇒f81=9-81=0 For absolute maximum and minimum value we need to look value of fxthrough out domain fx) For local maximum and minimum we need to look values of f(x) in open interval Absolute maximum is 9 ast x=0 Absolute minimum is Does Not exist Local maximum Does not exist Local minimum Does Not exist Hence absolute maximum value :9absolute minimum value:DNELocal maximum value:DNELocal maximum value : DNE