5. Let f (t) = 2t – 4. %3D А. Sketch or provide the graph of the function f on the interval [0,5]. Given A(x) = S ƒ(t)dt, evaluate the following. Explain: i. A(4) ii. А(3) iii. A' (4) B.

During a nine-hour snowstorm, it snows at a rate of 1 inch per hour for the first 2 hours, at a rate of 2 inches per hour for the next 6 hours, and at a rate of 0.5 inch per hour for the final hour. Write and graph a piecewise-defined function that gives the depth of the snow during the snowstorm. How many inches of snow accumulated from the storm?

Describe why the horizontal line test is an effective way to determine whether a function is one-to-one?

Find the slope of the line at the point x = 2 for the function f(x) = x ^ 2 * (3x - 2) 12 16 40 24 8 28

A function and its graph are given. Fx) = + 4x - 20x - 20 250 200 150 100 50 -10 -5 - 50 (a) From the graph, estimate where f"(x) > 0. (Enter your answer using interval notation.) Estimate where f"(x) 0. (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 f'(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

Level curves (isothermals) are shown for the water temperature (in °C) in Long Lake (Minnesota) in 1998 as a function of depth and time of year. Estimate the temperature in the lake on October 7 (day 280) at a depth of 5 m and on June 9 (day 160) at a depth of 10 m. X°C (day 280 and depth 5 m) X°C (day 160 and depth 10 m) Enter a number. Depth (m) 0 sti 10- 15+ 12 16 + 120 20 160 20 Day of 1998 16 200 240 280

A function with two curves, three closed points, and three open points is graphed on the x y coordinate plane. The first curve begins at the closed point (0, 2) increases to the open point (1, 4) decreases to (2, 2) increases to (4, 5) decreases to (5, 3) then turns sharply and increases to the closed point (6, 4). The second curve begins at the open point (6, 3) and decreases to the open point (7, 1). The closed point (1, 3) is graphed.

The graph of the function f(x) is shown below. It consists of a semicircle and two straight line segments. 150 + -3 -2 y 3 2 -1 1 2 (b) Which of the following numbers is the smallest: ƒ' (−3.95), ƒ' (−1.5), ƒ' (−0.05), ƒ' (1), ƒ' (3.05)? 3 5 X