Question

Can someone please help, I don't know how to do this at all...

Find the derivative of f(x) = -12x^2 + 9x at x = 6.

Answer 1

The equation is a standard polynomial function, so we can apply the power rule.
Assuming you don't know what is it:
The derivative of x^n is:
\[(n)x ^{n-1}\]
Where n is a number greater than 0.

So applying the power rule:
f'(x) = -24x + 9

For the power rule, we can ignore constants, so we essentially do nothing with the -12 and leave it as it is.

Then we plug in 6 into f'(x).

Answer 2

Since I don't think I covered constants and the power enough:
-12x^2's derivative is equal to -12 * the derivative of x^2 = -12 * 2x = -24x

Doesn't matter if it's -12, 50, 100, 20, etc. We can do this for any integer.

Answer 3

Alright, so the we have...

-24x+9x
-24(6)+9(6)
-90

Answer 4

I got -90 also, so confirming you're right.

Answer 5

No wait, you put the wrong derivative. It's -135, because the derivative of 9x is 9, not 9x.

Answer 6

Now, I'm just confused...

Answer 7

A derivative is the slope of an equation. So, for 9x, if we draw the graph, we can see that it's a straight line with a slope of 9.

Answer 8

The slope is constant at all pts on the line, so we put 9 as the derivative of 9x.

Answer 9

OhKay then...