Note: You do not need a calculator to solve this problem. In this question, we'll find the extreme values of the function f(x) = −6e cos x over the interval [0, 1], and the locations where they occur. (a) List the x-values of all critical points and endpoints. x = (b) Since we're asking for global extrema over a closed interval, we know that a global max and a global min are guaranteed to exist, and they'll exist at one of the locations you listed in (a). Find the value of f at each of the points you listed. It's not obvious, without a calculator, which values are the largest and which are the smallest. So, use what you know about graphing to help you determine the values below. Absolute minimum value: located at x = ' Absolute maximum value: 6e^(pi) located at x = pi 1

bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.

Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.

The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is given by A(t)=a(e)rt, where a is the amount ofprincipal initially deposited into an account thatcompounds continuously. Prove that the percentageof interest earned to principal at any time t can becalculated with the formula I(t)=ert1.

Use your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.

Please solve the following question and do it in steps with each explaining what it is. Please also explain how to solve the actual problem.

find the a bsoute extrema for the function 5 (x )=9rX - 3x an the given intervalOL XH

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A series of locks manages the water height along a water source used to produce energy. As the locks are opened and closed, the water height between two consecutive locks fluctuates. The height of the water at point B located between two locks is observed. Water height measurements are made every 10 minutes beginning at 8:00 a.m. It is determined that the height of the water at B can be modeled by the function f(x)=−13cos(πx60−5π12)+24, where the height of water is measured in feet and x is measured in minutes. What is the maximum and minimum water height at B, and when do these heights first occur? Drag a value or time into each box to correctly complete the statements.