Question

help

Answer 1

@Vocaloid is 1 c?

Answer 2

@Hero

Answer 3

@Shadow plz help

Answer 4

Check your messages

Answer 5

@Vocaloid

Answer 6

C for the first question is incorrect

Answer 7

here is an example of the process of the problem if you already had \(a\) and \(b\)
http://mathcentral.uregina.ca/QQ/database/QQ.09.04/louise1.html

of course, without knowing \(a\) and \(b\) makes this problem more confusing

Answer 8

I'll list how the general process for this kind of problem first, then we can plug in specific numbers:

\(\rightarrow\) (Step 1) First, we want to take the first and second derivatives of \(y\)
what do you get?

\(\rightarrow\) (Step 2) Next, the question asks about the inflection point
Inflection points are where the second derivative, \(y''\), equals zero
(we solve for x in terms of a and b)

\(\rightarrow\) (Step 3) Then, we plug in the mess of what x equals into the first derivative and get another expression made up of a's and b's

\(\rightarrow\) (Step 4) Take a step back now, let's consider the information they gave us:
that \(y'(1) = 9\) and \(y''(1) = 12\)
when we plug this into the derivatives we calculated in the first step...
\(y'(1) = 9 = 3a(1)^2 + 2b(1)\)
and
\(y''(1) = 12 = 6a(1) + 2b\)
(notice I plugged in x = 1 which might be why it looks a little weird)

Then you can solve the system of two equations to get values for a and b

\(\rightarrow\) (Step 5) And now for the mess...
You plug in your values of a and b into the thing you got from (Step 3). This will be the slope of your tangent equation

\(\rightarrow\) (Step 6) Also plug in the a and b into the thing you got from (Step 2). This will result in an x = something which you can plug in to the original equation to get a y value.
This will give you your (x, y) coordinates for where your tangent line goes through

\(\rightarrow\) So from (Step 5) and (Step 6) you now have a slope and a point which your line goes through. You can use the point-slope form, or slope-intercept form to get the equation of your line.


As you can see, this has been a lot of steps and can get a bit confusing. Let me know if you're stuck on any part of this. Although, I feel like it will make a lot more sense once we start plugging in numbers.