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You can calculate what each of those four terms are.

Hint:

You'd need to:

-Differentiate w(x) with respect to x, to obtain an expression for w'(x)

-Find the values of x for which w'(x) = 0

-Substitute these values of x into your equation for w''(x) to determine which values of x correspond to a minimum and which correspond to a maximum

Correct.

One other approach you could have used is to calculate w'(x) to determine its stationary points, then evaluating w''(x) at these points to determine which of these is a maximum and which of these is a minimum. However, the approach taken above is a lot quicker and perhaps more intuitive.

mathland wrote:

(-3/a) + (4/b) = 1

mathland wrote:

I say a = d and b = d.

What happens when you substitute a = d and b = d into the equation above?

For part (a) you're asked to determine the acceleration in terms of t, so you'll also need to calculate s''(t).

Other parts are correct.

Yes, you need to find the second derivative and then add that to y.

Correct.

Correct.

Yes -- finally, what are the maximum and minimum values of w(x)?

You might like to use the fact that:

sec(t)*cos(t) = 1

and

sec(t)*sin(t) = tan(t)

Can you see why these are true?

You have

mathland wrote:

(-3/a) + (4/b) = 1

and

mathland wrote:

I say a = d and b = d.

How can you eliminate a and b to determine the (numerical) value of d?

mathland wrote:

Taking the derivative in terms of t, I get

V = -(1/8) sin(t).

I don't know how to find the maximum speed from this point on.

What is the range of possible values of sin(t)?

What is the range of possible values of -(1/8)sin(t)?

What is the range of possible values of V?

mathland wrote:

For part (a), I must evaluate R(t) at t = 1 and t = 2. Yes?

No. You have been given four dates, not two -- so what are the values of t at these dates?

mathland wrote:

For part (b), I get R'(t) = cos (t) + 0.3.

Correct.

mathland wrote:

For part (c), what particular value of t are you taking about?

The value of t that is mentioned in the question.

What are the smallest and largest values of 2 + cos(x)?

For part (a), what is the value of t for the range of dates you've given?

For part (b), you want to calculate the rate of change of R(t) with respect to t. In other words, you'll need to determine R'(t).

Part (c) just involves calculating R'(t) at that particular value of t.

You have been given the displacement, s, of the object in terms of time, t. If you differentiate this with respect to t, you'll get the object's velocity in terms of time. How would you find the maximum speed from here?

Note that this equation describes a phenomenon known as simple harmonic motion -- if you've come across this before (and know the sort of motion it's describing), you can have a think about how the object's speed varies between its points of maximum and minimum displacement, which is a shortcut to the answer.

To find the minimum and maximum value of w, there are a few different approaches you could take.

The question is asking: what are the smallest and largest possible values of ?Here's a starting point: what are the smallest and largest possible values of ?