Example 12: Sketch a graph of the function f(x) = x¹ = 4x³ + 10 using the following steps. 32 (a) Identify where the extrema of f occur. (b) Find the intervals on which f is increasing and the intervals on which f is decreasing. (c) Find where the graph of f is concave up and where it is concave down. (d) Sketch the general shape of the graph for f. (e) Plot some specific points, such as local maximum and minimum points, points of inflection, and intercepts. Then sketch the curve.

Q: Water runs into a vase of height 30 centimeters at a constant rate. The vase is full after 5…

A: Water runs into vase of height 30 centimetres at a constant rate. The vase is full after 5 seconds.…

Q: Roadways are crowned to let rain run off to the shoulders of the road, as illustrated in the…

A: Using the data given in the question we need to check which of the statements A,B,C,D,E are True.

Q: Move the slider h so that the graph of y= f(x) in the answer box = x² gets shifted to the right 3…

A:

Q: A and B are points on the graphs of functions y1 and y2, respec-tively. Find the corresponding point…

A: Given information: y=y1+y2 A and B are points on the graphs of functions y1 and y2 A=π,-0.5B=π,-1

Q: Step 1 To sketch the graph of f(x) = 4x - x2, first construct a table of values by evaluating the…

A:

Q: Move the sliderk so that the graph of y = 2" gets shifted up 3 units. Then type the new function,…

A: We have to slide the k such that graph shifted 3 unit up.

Q: Consider the graph of a function f shown here: 3 (c) 6 ƒ(9) — ƒ(6) 9-6 (d) f'(3) ? 9 Using the…

A: From the given graph

Q: Sketch the graph of f(x.y) = 5x +3y - 15. State the domain and range of the function Which of the…

A: Given the equation of the plane fx=5x+3y-15 which can be written as z=5x+3y-15. Take arbitrary…

Q: Consider the function f(x) = 1/2(ax)2 − ax, a ≠ 0. (a) Determine the changes (if any) in the…

A: Part (a)

Q: Use the given graph of f to select the graph for the following function. y= {2x) 6 4 + (-4, 2) 2 +…

A: Given : graph of f(x)  To find the graph of y = f(2x)

Q: The graphs of two functions, f and g, are illustrated. Use the graphs to answer parts (a)–(f).…

A: (f+g)x = f(x)+g(x) (f-g)x = f(x)-g(x) fg(x) = f(x)g(x) f/g(x)=f(x)/g(x)