Question

Can someone help me with this multi question problem.

Answer 1

Question 1: Explain why A(3)=27
Question 2:Write an expression for A(x).
Question 3:Find the maximum value for A(x).
Question 4: Suppose that the point (x,0) was moving to the right at 0.5 cm/sec. How fast is A(x) changing when x=3?

Answer 2

@smokeydabear can you please help me again

Answer 3

can you please help me

Answer 4

@tcarroll010 can you help me and do you understand

Answer 5

All I looked at so far was the first question, but that one looks quite clear. I'll show why in next message.

Answer 6

ok

Answer 7

The rectangle is (6 - x) wide (from (6, 0) distance to (x, 0) ). Just subtract the first coordinate. Similarly, the height is x^2. So, the area is (6 - x)(x^2).

A(x) = (6 - x)(x^2) = 6x^2 - x^3

So,

A(3) = 6(3^2) - 3^3 = 54 - 27 = 27.

Answer 8

It looks like I also answered question #2 with the above.

Answer 9

Question #3:

A'(x) = 12x - 3x^2 = 3x(4 - x)

That is 0 when x is 0 or 4. And since this derivative equation is a parabola opening downwards, we have a maximum at x = 4.

Answer 10

Question #4:

dA/dt = (dA/dx)(dx/dt) = (12x - 3x^2)(0.5)

At x=3,

[12(3) - 3(3^2)](0.5) = 4.5

Answer 11

All good now, @mathlover6 ?

Answer 12

got thanks sorry for not getting back sooner but I was trying to make sense of while you posted

Answer 13

sorry I am still making sense of it all

Answer 14

np