Finding derivatives?

Question

How do I find the derivative of f(x) = 10x - 1.86x^2 when x=a. Do I need to plug the "x" with "a"? Any help is appreciated. Thanks.

Answer 1

How you mean this makes a huge difference.

If you want to derive f(x) first over 'x', then evaluate the derivative at 'a'... that is how the guy above me did this. And how I interpret this too.

f'(a) = d/dx f(x=a) = d/dx 10(x=a) - 1.86(x=a)^2 = 10 - 3.72a

If, on the other hand, you want to evaluate the function at 'a', first, then derive over 'x', this is a whole different story.

f(a) is a constant, therefore its derivative over x is 0

Answer 2

Hi,

Assuming I understand your question, correctly, first take the derivative of f(x) = 10·x - 1.86·x² to get

f'(x) = 10 - 3.72·x

Now, plug in a to get the same expression, only the xs are replaced by as.

In other words, the final result will be

f'(a) = 10 - 3.72·a


James :-)

Answer 3

the new equation is 10a-1.86a^2 right?
so y=10a-1.86a^2

--> dy/dx=10(da/dx) - 3.72a(da/dx) <--

you still have to find da/dx

i think this is it....

Answer 4

f(x) = 10x - 1.86x^2

f(x) = 10 - 3.72(a)

I don't know know.