Very strange question for derivative

peacemaster

1. The problem statement, all variables and given/known data

The question in it's complete wording:

Consider the following curve.
y = 8 + 5x2 - 2x3.

Find the slope of the tangent to the curve at the point where x = a.


2. Relevant equations

(y2-y1)/(x2-x1) where x2=x1+dx and the limit of dx is approaching zero and y2=f(x+dx).

3. The attempt at a solution

Well, this is the really hard part because they don't tell you what a is. Basically, this is a curve and they say find the slope of the tangent at the point where x=a, but that point could be anywhere on the entire curve.

Don't worry, I didn't misread the question. There isn't any info lingering elsewhere. A is not defined anywhere in the problem.

So my question is... what gives? Am I missing something here?

Thank you so much for any help,

Peacemaster

HallsofIvy

Better notation: y= 8+ 5x^2- 2x^3. Even better is to use "LaTex": [itex]y= 8+ 5x^2- 2x^3[/itex]

You have written two contradictory things. You say "at the point where x = a" and then, later, "find the slope of the tangent at point a". Is "a" a number or a point?

If a is a number, "x= a", then I don't see what the difficulty is. If the problem had said "at the point where x= 0" or "at the point where x= 2" what would you have done? Whatever you do with "0" or "2", do the same with "a".

peacemaster

Wow, good catch. I didn't realize the contradiction. The way I stated the problem is all the info given to me by the question.

The problem asks to find the slope of the tangent at the point where x=a. A is an x value, not a point. The problem does not tell me what a is.

I will edit the original post to reflect the clarification.

What would you do with the problem the way I originally posted it?

Thanks,

Peacemaster

VietDao29

You can treat a as any number. As HallsofIvy has already pointed out.

a can be 0, 2, 3, or 1/3, blah blah blah. It does not matter, you just think of a as some number that you don't know, or maybe don't need to know.