The function in the figure below has f(2) = 22 and f?'(2) = 1.5. Find the coordinates of the points A, B, C.

Question

The function in the figure below has f(2) = 22 and f '(2) = 1.5. Find the coordinates of the points A, B, C.

 

The picture shows a concave down graph with c, A, and B on the tangent line. Point A is where the tangent touches the graph and has an x value of 2. B is above A on the tangent line but not on the graph. the x value or value given below it is 2.2. For C, it is below A only on the tangent line. It's x/below value is 1.9.

point A (x, y) = I think this is (2,22)
point B (x, y) = 
point C (x, y) = 

For B and C I don't know how to find the y values. I assume the x values are the ones below it, but I don't know where to go from there. Please help me, I am very confused.

Answer 1

After I drew this on my paper using the description you provided, I obtained a tangent line to the graph that has a positive slope.  What we need to do is find the equation of that tangent line.

 

f'(2)=1.5          means that slope of the tangent line at x=2 is 1.5

 

The given coordinate of the original point is (2, 22).

 

We can use the point-slope form of a line to find the equation of this tangent line.

 

y = m(x - x₁) + y₁

 

y = 1.5(x - 2) + 22

 

y = 1.5x - 3 + 22

 

y = 1.5x + 19

 

 

Use this equation to find the y-coordinates of A, B, and C.

 

A = 1.5(2) + 19

 

B = 1.5(2.2) + 19

 

C = 1.5(1.9) + 19