SOLUTION: Find the equation of the tangent line to the curve, y = x^3

SOLUTION: Find the equation of the tangent line to the curve, y = x^3 - 3x^2 + 5x = 2 that has the least slope.

Question 1082928: Find the equation of the tangent line to the curve, y = x^3 - 3x^2 + 5x = 2 that has the least slope.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

doesn't make any sense, so I figure you either meant +2 and you failed to hold the shift key when you pressed the +/= key, or you meant -2 and you simply pressed the +/= key instead of the _/- key. Either scenario being equally likely, I'm going to do the problem for the following function:

Where

is an arbitrary real number constant.

The minimum slope tangent to the original function will occur at the point where the first derivative has a minimum.

Which has a zero at

For the original function

Hence, the point of tangency is

So you want an equation of a line that passes through the point

with a slope of 2.

Once you figure out whether

,

Then you can complete the problem.

By the way, the question was also worded incorrectly in the first place. You cannot find THE equation of a line. You can only find AN equation of a line.

John

My calculator said it, I believe it, that settles it

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