Question

Find the derivative of f(x) = -12x2 + 9x at x = 6. (2 points)

Answer 1

We can split them up
dy/dx-12x²=-12 times dy/dx x²=-12 times 2x=-24x

dy/dx9x=9 times dy/dx x=9 times 1=9

so

f'(x)=-24x+9
f'(6)=-24(6)+9
f'(6)=-144+9
f'(6)=-135

Answer 2

Answer:

$\frac{dy}{dx}|_{x=6}=-135$

Step-by-step explanation:

Given : Function $f(x)=-12x^2+9x$

To find : The derivative of the function at x=6?

Solution :

Function $y=-12x^2+9x$

Derivative w.r.t x,

$\frac{dy}{dx}=-(2)12x^{2-1}+(1)9x^{1-1}$

$\frac{dy}{dx}=-24x+9$

Now, The derivative at x=6 is

$\frac{dy}{dx}|_{x=6}=-24(6)+9$

$\frac{dy}{dx}|_{x=6}=-144+9$

$\frac{dy}{dx}|_{x=6}=-135$

Therefore, $\frac{dy}{dx}|_{x=6}=-135$