Was my professor right to count me off?

[Wishingwell]

Homework Statement

I recently was counted off during a math quiz stating that I made a mistake in my arithmetic regarding the derivative of a function using the limit approach. (The long way with the lim h->0)

The equation was f(x) = -16x^2 + 20x and I was suppose to find f'(x) using the limit approach

Homework Equations

I am very sure I did everything right since my final answer was -32x + 20 but during my work there was one step he counted me off 1 letter grade for.

Doing the work you get down to a step that looks like this:

(-32xh - 16h^2 + 20h)/h

At this point I divided each term by h to get -32x -16h + 20 where I plugged in 0 for h.

However this was incorrect, it was apparently algebraically wrong as I was suppose to factor out an h from each term and then divide by h. I have always been taught to divide by h and assumed this was is an acceptable way to do it.

Was it any wrong to lose credit for dividing by h instead of factoring and then dividing? If not, can anyone explain and I can maybe send this to my professor to get some credit back.

The Attempt at a Solution

See above

 

[mathie.girl]

I honestly couldn't imagine anyone taking off points for that, unless you were told specifically to include that step (in which case I don't think you'd have much of an argument).

I encourage students to factor and then cancel because so many write something like $$\frac{xh + 6}{3h} = \frac{x+6}{3}$$. So I tell them that unless you can factor it out of every term, you can't cancel it. However, I wouldn't expect them to write that step if they were mathematically mature enough to see it themselves. The same way I wouldn't expect someone to say $$\frac{12}{20} = \frac{3*4}{4*5} = \frac{3}{5}$$ after they got out of elementary school.

I would definitely ask about it. However if you're asked to show working, I suppose your teacher is able to decide how much work he wants to see.

 

[Wishingwell]

I honestly couldn't imagine anyone taking off points for that, unless you were told specifically to include that step (in which case I don't think you'd have much of an argument).

He explained that it was "algebra" and didn't need to be explained since we were suppose to know that factoring was the correct way to do it.

 

[mathie.girl]

He explained that it was "algebra" and didn't need to be explained since we were suppose to know that factoring was the correct way to do it.

Factoring was a correct way to do it (though that doesn't imply to me that it needs to be shown, especially in a calculus course). Alternatively, you could have just as easily have done:

$$\frac{-32xh - 16h^2 + 20h}{h} = \frac{-32xh}{h} - \frac{16h^2}{h} + \frac{20h}{h} = -32x - 16h + 20$$

Which would pretty much just be splitting up and cancelling (and possibly more similar in idea to what you did).

Does he require you to show steps like this, which should also be required if you were to show all algebraic steps?

$$5x + 16y - 2x = 5x -2x + 16y = 3x + 16y$$

I can tell you that to me it seems like a surprising level of detail to require of a calculus student and certainly not something I'd take points off for, however it could be construed as a missing step. So honestly I'm not sure what to tell you about how to handle your prof. Good luck getting it straightened out!