Find the derivative of f(x) = 6x + 2 at x = 1.

Question

psymon · Answer

Basically, when you take the derivative you get just a number. When that happens, the derivative is the same everywhere. The reason is because the derivative basically helps you find the slope at a point. But when you take the derivative of this, you get 6. Well, if derivative gives you slope, then this basically is telling the slope is ALWAYS 6. So your answer i just 6. And your answer would be 6 no matter what x you gave me.

anonymous · Answer

Thank You so much. So, 7/x at x =1 would be 7.

psymon · Answer

Nope.

psymon · Answer

The derivative of 7/x doesnt make x disappear. You'll still have an x-alue to plug x = 1 into

debbieg · Answer

Well, 7/x at x=1 WOULD be 7. But that has nothing to do with the problem you stated. :)

psymon · Answer

Eh, itd be -7.....?

anonymous · Answer

would it be -7 because that makes the x disappear?

debbieg · Answer

If you are talking about the derivative of a DIFFERENT function, y=7/x, the reason it isn't the same as the original problem is that your first function is LINEAR.

For a linear function (an equation for a line), the derivative is simply the slope of the line, which is a constant.

But, for y=7/x, the function is NOT LINEAR, and the slope is not constant... it depends on x.

psymon · Answer

Yeah, its basically what Debbie said, its the difference between having a linear function or not. 7/x isnt linear.

debbieg · Answer

Sorry, @Psymon , when I said "7/x at x=1 WOULD be 7" I meant, quite literally, the function y=7/x evaluated at x=1, would be 7.

That's different than the derivative of y=7/x, at x=1. :)

psymon · Answer

Fair enough, lol.

anonymous · Answer

Okay. It makes sense now, because at first I wasn't understanding why it was one answer for the first question, but the complete opposite for the second question. Nonetheless, I do comprehend.

debbieg · Answer

If what you want is the derivative of y=7/x, at x=1, then you have to first compute the formula for the derivative, and then plug x=1 into THAT.

As @Psymon said, you will get f'(1)=-7

anonymous · Answer

Thank you for explaining.