8 questions

Consider the function f(x) = 5x - 10x + 3, 0 5 x 5 8. The absolute maximum of f() (on the given interval) is at a = and the absolute minimum of f(a) (on the given interval) is at x = nunction Wales mud.. Find all critical values for f(x) = (z + 9)'(z + 8)" The critical values occur at x = . (Enter your answers separated by commas) Consider the function f(x) = 2x - 15x2 - 36x + 10 on the interval [ - 6, 9]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval ( - 6, 9) such that f' (c) is equal to this mean slope. For this problem, there are two values of c that work. Round answers to 3 decimal places. The smaller one is and the larger one is Consider the function f() = - on the interval [5, 6]. Find the average or mean slope of the function on this interval. Leave as an integer or reduced fraction. By the Mean Value Theorem, we know there exists a c in the open interval (5, 6) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it, to 3 decimal places. E1pt Consider the function f() = 8va + 3 on the interval [1, 8). Find the average or mean slope of the function on this interval, to 3 decimal places. By the Mean Value Theorem, we know there exists a c in the open interval (1, 8) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it, and round to 3 decimal places. Consider the function f(z) = 6e on the interval [0, 4]. 15 14 13 12 11- 10 Q Find the average or mean slope of the function on this interval. Enter at least 4 decimal places in your answer. By the Mean Value Theorem, we know there exists a c in the open interval (0, 4) such that f' (c) is equal to this mean slope. For this problem, there is only one c that works. Find it. Enter at least 4 decimal places in your answer. if a rock is dropped from a height of 222 ft, its position t seconds after it is dropped until it hits the ground is given by the function s(t) = - 16t + 222 Round values below to 3 decimal places. How long does it take the rock to hit the ground? seconds Find the average velocity of the rock from when it is released until when it hits the ground. feet per second What time after the rock is thrown will its instantaneous velocity be equal to its average velocity? (Apply the Mean Value Theorem) seconds after it is thrown Consider the function f(a) = 5 - 2x on the interval [ - 4, 3]. Find the average or mean slope of the function on this interval, i.e. f(3) - f( -4) 3 - (-4) By the Mean Value Theorem, we know there exists a c in the open interval ( - 4, 3) such that f'(c) s equal to this mean slope. For this problem, there is only one c that works. Find it