Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3xVx + 2 4 - 10 Step 1 The minimum and maximum of a function on an interval are the extreme values, or extrema (the singular form of extrema is extremum), of the function on the interval. In the given problem, the extremum occurs when x = 3 The specified function is f(x) = -3xx + 2 = -3x(x + 2)1/2 Differentiate f(x) using the product rule. f "(x) = -3x (x + 2) J + (x + 2)1/2. ([

Find the derivative of the function. f(x) = (2x−8)4(x2 + x + 1)5     (note: previous answers not correct)

Use technology to sketch the graph of the given function. f(x) = x4 – 2x3 + x² - 2x + 1 Indicate any extrema. The coordinates of the extrema should be accurate to two decimal places. [HINT: To locate extrema accurately, plot the first derivative.] (If an answer does not exist, enter DNE.) (х, у) %3D (1.40, – 1.49 minimum Indicate any points of inflection. The coordinates of the points of inflection should be accurate to two decimal places. [HINT: To locate points of inflection accurately, plot the second derivative.] (Order your answers from smallest to largest x. If an answer does not exist, enter DNE.) (x, y) 0.60, – 0.55 X (x, y) = ( 0.21,0.78 * )

A function and its graph are given. f(x) = + 4x2 - 20x – 20 y 250 200 150 100 50 - 10 -5 5 –50 (a) From the graph, estimate where f"(x) > 0. (Enter your answer using interval notation.) Estimate where f"(x) o. (Enter your answer using interval notation.) Find where f"x) < 0. (Enter your answer using interval notation.) Find where f"(x) = 0. (Enter your answers as a comma-separated list.) Find where r(x) has its relative maxima and relative minima. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) relative maxima relative minima