Finding minimum and maximum values of s(t)= -5t^3-12t^2+9t-11

[huggy99]

1) s(t)= -5t^3-12t^2+9t-11

I know I have to make the first derivative = 0 but I don't know how I'm supposed to factor. If someone could help that would be amazing I've been trying to solve this for a while now.

2) c(n)= 3n^2-25n+650

I have to find the maximum but I can only get a minimum value. Thanks.

 

[Deleted member 4993]

1) s(t)= -5t^3-12t^2+9t-11

I know I have to make the first derivative = 0 but I don't know how I'm supposed to factor. If someone could help that would be amazing I've been trying to solve this for a while now.

What is the first derivative of the given function?

2) c(n)= 3n^2-25n+650

What is the first derivative of the given function?

What is the second derivative of the given function?

I have to find the maximum but I can only get a minimum value. Thanks.

.

 

[stapel]

1) s(t)= -5t^3-12t^2+9t-11

I know I have to make the first derivative = 0 but I don't know how I'm supposed to factor.

They were supposed to have taught you factoring back in algebra. To learn now, try here. A good first step, of course, will be to divide through by -3, to get a positive quadratic with smaller coefficients.

2) c(n)= 3n^2-25n+650

I have to find the maximum but I can only get a minimum value.

Back in algebra, they were also supposed to teach you about graphing quadratics. You can learn about this here. You will quickly see that quadratics only ever have one extreme point, so you'll either have a maximum or else a minimum, but never both. So your answer for "maximum" here would be "none".

 

[Ishuda]

1) s(t)= -5t^3-12t^2+9t-11

I know I have to make the first derivative = 0 but I don't know how I'm supposed to factor. If someone could help that would be amazing I've been trying to solve this for a while now.

2) c(n)= 3n^2-25n+650

I have to find the maximum but I can only get a minimum value. Thanks.

One of the things you should pay attention to is whether you are being asked for global maxima (minima) or relative maxima (minima). If a polynomial has an odd degree there is no global maximum nor is there a global minimum and, as stapel implied, if the order of the polynomial is even, it either has a global maximum or a global minimum but not both. Hint, look at the behaviour of the value of the polynomial for very large values both positive and negative.