SOLUTION: Find the value of x for which the tangent line to {{{y=2x^2 + 1}}} will be parallel to the tangent line to {{{y = 4ln(x)

SOLUTION: Find the value of x for which the tangent line to {{{y=2x^2 + 1}}} will be parallel to the tangent line to {{{y = 4ln(x) - 3}}}

Question 1153638: Find the value of x for which the tangent line to will be parallel to the tangent line to
Found 2 solutions by greenestamps, jim_thompson5910:
Answer by greenestamps(13195) (Show Source): You can put this solution on YOUR website!

The slopes are equal when

or

The second function is undefined at x=-1; so x=1 is what we are looking for.

For the first function,

For the second function,

The slopes of the two graphs are the same at (1,3); and the two graphs are tangent to each other at that point.

At x=1, the slope of both graphs is 4; the line with slope 4 passing through (1,3) is

A graph, showing the two curves and the common tangent line:

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

The tutor @greenestamps has a great set of steps and the correct final answer. The only issue I see is that somehow 4ln(x)-3 turned into 4ln(x)+3. This will mean the two functions do not intersect at (1,3). Other than that, everything else is perfect.

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