Question

Calculus help plz... pic below

Answer 1

Sandy: How about starting out with #5 and writing out what you already know about this problem?
Here's an outline of what I did:
a) by multiplying out the two factors of the function, or simply by ogling it, we can determine the dominant term. What does that term look like?
b) The sign of the dominant term tells us a lot. If the dominant term involves an even power of x and the sign of that term is (-), the graph will be mostly concave DOWN. Why? Will the graph of y = (x^3)*(3-x) be mostly concave up or mostly concave down?

Answer 2

(c) What are the critical values of the function? In other words, what is the derivative, dy/dx, and if we set that equal to 0, what are the roots of this equation?
(c) Do any of the roots represent the location of a local max or min? Find the second derivative and evaluate it at each of the critical values. If the result is (-), the graph is concave downward at that x value. If the result is (+), then what? If the result is 0, then what?
Hope this helps you to solve and answer the question on your own. If not, please ask specific questions about what you need to know to solve it.

Answer 3

do i have to find the derivative of it to know or just graph it? for #5

Answer 4

Sandy: Strictly speaking, you don't have to find the derivative of this function to graph it, but using the first and second derivatives is generally much faster and more efficient than is picking x values at random and calculating the associated y values to obtain points on the graph.

Answer 5

well i am allowed to use a graphing calculator

Answer 6

Have you tried graphing y = (x^3)*(3-x) yet? I used my calculator (an old TI-83) to do so, and could see immediately from the resulting graph that this function has both a local and an absolute maximum (at the same point).

Answer 7

Are you in an algebra course or in calculus?

Answer 8

calculus

Answer 9

Then I'd strongly suggest you become comfortable with finding the first and second derivatives to assist with graphing any but the simplest of functions. In the long run it'll be much faster.

Answer 10

hmm.. i never been taught how to do it that way

Answer 11

Hope I'm not going too far ahead in this game. Which method or methods have you learned for graphing functions such as (x^3)(3-x)?

Answer 12

anyways would the answer be E) I and III?

Answer 13

I'll answer that if you want, but I'd feel a lot better dealing with methods of solution than answers.

Answer 14

i just wanted to double check my answer with you

Answer 15

Well, would you mind explaining the reasoning that led you to conclude that this function has a local/relative minimum?

Answer 16

no i think it has an absolute maximum and a relative minimum

Answer 17

Sandy, this function does have an absolute max. What is it? But I was asking why you think it also has a relative minimum. What does "relative min" mean to you?

Answer 18

I am not sure how to explain it :/

Answer 19

As you can probably guess, I've concluded that this function does NOT have a relative minimum.

Have you been able to graph this function? If so, could you describe in words what it looks like to you?

Answer 20

it looks almost like a parabola