If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x) g(x) .

Question

If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x)

and v(x) = f(x)

g(x)

.

The x y-coordinate plane is given. There are 2 functions on the graph.

1. The function labeled f enters the window in the second quadrant, goes down and right, sharply changes direction at the point (−1, 1.6), goes up and right, crosses the y-axis at y = 1.8, passes through the point (1, 2), passes through the point (6, 3), and exits the window in the first quadrant.
2. The function labeled g enters the window in the third quadrant, goes up and right, crosses the x-axis at x = −2, crosses the y-axis at y = 2, passes through the point (1, 3), sharply changes direction at the point (2, 4), goes down and right, sharply changes direction at the point (3, 1), goes up and right, passes through the point (6, 4), and exits the window in the first quadrant.

(a)

Find u ′(1).

(b)

Find v ′(6).

Answer 1

Hi Oa D.,

Your question appears to be garbled a bit, perhaps by improper entry into Wyzant. u(x) and v(x) seem to be identical. You should always check your question after you submit it, and enter any additional material facts by comments if that happens. There is always a way around the limitations of Wyzant, by using sufficient quantities of parentheses, and ^ as exponent symbol (takes a parenthesized expression as argument, for clarity). Is one of those supposed to be f(x)/g(x) ? or f•g(x) ? No one can guess. No one can read your mind.

-- Cheers, --Mr. d.