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

`(dy)/(dx)|_(x=6)=-135`

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,

`(dy)/(dx)=-(2)12x^(2-1)+(1)9x^(1-1)`

`(dy)/(dx)=-24x+9`

Now, The derivative at x=6 is

`(dy)/(dx)|_(x=6)=-24(6)+9`

`(dy)/(dx)|_(x=6)=-144+9`

`(dy)/(dx)|_(x=6)=-135`

Therefore,
`(dy)/(dx)|_(x=6)=-135`