If g'(x)=2, what is x?

[bubbles930]

Hi! I hope I am putting this in the right place - apologies if it's not!

My question is follows: the tangent line to the graph of g at the point (?,2) passes through (2,4). If ?′ (?) = 2 then what is ?? Draw a picture to illustrate.

Am I correct in saying that x is equal to 2x+c ? My logic is just doing the reverse of the derivative but I'm not sure.

Could anyone shed some light, and perhaps draw the graph?

Cheers.

 

[Steven G]

No y=2x+c. Now use the given point to find c.

 

[HallsofIvy]

As Jomo said, the function describing the tangent line is y= 2x+ c. Since it passes through (2, 4), we must have 4= 2(2)+ c so c= 0. The tangent line is given by y= 2x. Now, what value of x are you trying to find? If you mean the x-value of the point at which that line is tangent to y= g(x), that depends upon what "g" is! Just knowing the derivative of g at a single point is not sufficient.

 

[Dr.Peterson]

My question is follows: the tangent line to the graph of g at the point (?,2) passes through (2,4). If ?′ (?) = 2 then what is ?? Draw a picture to illustrate.

The problem might be clearer if you replace x with some other variable, say k, since x will be used in the equation of the line. Here is the problem rewritten:

The tangent line to the graph of g at the point (k,2) passes through (2,4). If ?′ (k) = 2 then what is k?​

Write the equation of the line with slope 2 through (2,4), then find the value of k such that (k,2) is on the line.