Question

if f(x) = 2x^3 + 3x^2 - 36x + 11 , for what two values are the slope of the tangent line horizontal

Answer 1

please, calculate the first derivative of f(x), first

Answer 2

@cleetus779 do you know how to calculate the first derivative of f(x)?

Answer 3

yes, did so, then found the zeroes of that equation to be x=-3 and x=2

Answer 4

ok! those values are your answer!

Answer 5

should the be represented as a set {-3, 2}

Answer 6

if you want...

Answer 7

how else, like I wrote above?

Answer 8

please, note that if the tangent line is horizontal, then its slope is zero, so you can write that: "tangent lines of the function f(x) are horizontal at point x=2 and x=-3. Respectively values of f(x) are: f(2)=...and f(3)=..."

Answer 9

now you have to substitute x=2 and x=-3 into your function and then calculate, please the values f(2) and f(3)

Answer 10

@cleetus779

Answer 11

just asks for the x values at those points...do I need to?

Answer 12

I got: f(2)=-33, f(-3)=92
are they right?

Answer 13

so, it only asks at what values of x is the tangent line horizontal, the set above should be enough, shouldn't it?

Answer 14

since we found the derivative, and looked for where that value would be zero, those are the answers

Answer 15

yes I think, I have calculated the values f(2) and f(-3) for completeness only!

Answer 16

thanks

Answer 17

thanks!