179k views
2 votes
The function f is defined by f(x) = x/x+2 what points (x,y) on

the graph of f have the property that the line tangent to f at
(x,y) has slope 1/2?
a. (0,0) only
b. (1/2,1/5) only
c. (0,0) an

1 Answer

3 votes

Final answer:

The points on the graph of the function f(x) = x/(x+2) where the tangent has a slope of 1/2 are (0,0) and (-4,2), obtained by finding the derivative of the function, setting it equal to 1/2, and solving for x.

Step-by-step explanation:

To determine which points (x,y) on the graph of the function f(x) = x/(x+2) have a tangent line with slope 1/2, we need to find the derivative of the function, set it equal to 1/2, and solve for x. The derivative of the function f(x) gives us the slope of the tangent line at any point on the graph.

Derivative of f(x):

f'(x) = d/dx [x/(x+2)] which simplifies to f'(x) = 2/(x+2)^2.

We then set the derivative equal to 1/2 to find the x-values where the slope of the tangent is 1/2: 2/(x+2)^2 = 1/2.

Solving for x gives us two solutions: x = 0 and x = -4.

Plugging these back into the original function, we get the corresponding y-values; f(0) = 0/2 = 0 and f(-4) = -4/(-4+2) = -4/-2 = 2.

Therefore, the points on the graph where the tangent has a slope of 1/2 are (0,0) and (-4,2), which corresponds to option c.

Complete Question:

the function f is defined by f(x) = x/x+2 what points (x,y) on the graph of f have the property that the line tangent to f at (x,y) has slope 1/2?

a. (0,0) only

b. (1/2,1/5) only

c. (0,0) and (-4,2)

d.(0,0) and (4,2/3)

e. there are no such points

User Russell Zornes
by
7.8k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories