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#1 Re: Help Me ! » Chain Rule » Yesterday 04:10:02

You can calculate what each of those four terms are.

#8 Re: Help Me ! » Minimum & Maximum » 2021-05-05 10:56:55

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

#9 Re: Help Me ! » Minimum & Maximum » 2021-05-05 08:25:48

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.

#10 Re: Help Me ! » Using Intercept Form » 2021-05-04 20:54:28

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?

#11 Re: Help Me ! » Rectilinear Motion » 2021-05-04 18:56:53

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.

#12 Re: Help Me ! » Smallest Possible Integer » 2021-05-04 18:54:47

You want to find how many times you need to differentiate y until you end up with your original function y again.

#13 Re: Help Me ! » Show y" + y = 0 » 2021-05-04 18:50:31

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

#16 Re: Help Me ! » Minimum & Maximum » 2021-05-03 11:26:15

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

#17 Re: Help Me ! » Quotient Rule » 2021-05-03 11:11:57

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?

#18 Re: Help Me ! » Find Three Additional Points » 2021-05-03 11:09:27

Try plotting the point (3, -2) on a graph -- then draw a horizontal line through it. Once you've done this, can you identify some other points on the line?

#19 Re: Help Me ! » Using Intercept Form » 2021-05-03 11:07:43

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?

#20 Re: Help Me ! » Speed of An Object » 2021-05-03 11:05:41

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?

#21 Re: Help Me ! » Restaurant » 2021-05-03 11:00:59

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.

#22 Re: Help Me ! » Minimum & Maximum » 2021-05-03 10:57:05

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

#23 Re: Help Me ! » Restaurant » 2021-05-02 07:43:06

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.

#24 Re: Help Me ! » Speed of An Object » 2021-05-02 07:38:37

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.

#25 Re: Help Me ! » Minimum & Maximum » 2021-05-02 07:07:12

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
?

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