Help: derivative and critical #'s

[buffgilville]

I can't seem to find the f ' (x) of the following:

1) f(x) = -2x - ((128)/(x+9))

2) f(x) = (x+4)^2 (x-10)^3
(Find the number x at which the function f(x) = (x+4)^2 (x-10)^3 takes on an absolute minimum on the interval 4 < x < 10 (note: < means greater than or equal to )

 

[Fredrik]

1. It's just -2+128/(x+9)^2. Do you understand why?
2. Do you know how to take the derivative of a product of two functions?

 

[HallsofIvy]

I can't seem to find the f ' (x) of the following:

1) f(x) = -2x - ((128)/(x+9))

2) f(x) = (x+4)^2 (x-10)^3
(Find the number x at which the function f(x) = (x+4)^2 (x-10)^3 takes on an absolute minimum on the interval 4 < x < 10 (note: < means greater than or equal to )

The derivative of -2x is -2. To differentiate ((128)/(x+9) use the quotient rule.

To differentiate (x+4)^2 (x-10)^2 you will need to use the product rule.
(and the chain rule but the derivatives of both x+4 and x- 10 are 1 so it doesn't really show up.)