#### izzy0817

Stuck again (Headbang)...not sure what this question is asking me exactly, I've looking over all my class notes and I'm pretty sure we were never taught this. How exactly do I solve the:

Determine the equation of the tangent line to the graph of f(x) = -4x^2 + 11x - 2 at x = 2 that is parallel to the line y = 3x - 1.

#### Archie

You have more information than is necessary to complete the question. The given information gives you two ways to solve it.

First: you are given the equation of a line parallel to the tangent at $$\displaystyle x=2$$. To be parallel the tangent and this other line $$\displaystyle y=3x-1$$ must have the same slope. So we therefore know the slope of the tangent. We also know that the tangent passes through the point $$\displaystyle \big(2,f(2)\big)$$. Given the slope of a line and a point on the line, we can determine its equation using $$\displaystyle y - y_0=m(x-x_0)$$.

The second approach is similar, but involves using the derivative of $$\displaystyle f(x)$$ evaluated at $$\displaystyle x=2$$ to determine the slope of the tangent.

The odd thing is that the two answers are different, so there's a problem in the question. Perhaps the tangent should be at $$\displaystyle x=1$$. Or perhaps you are supposed to determine where the tangent is parallel to the given line.

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#### izzy0817

So confused still....I did the derivative and found -5-4h^2, which is -5-4(0)^2. So the final answer I got was -5, is that even correct? I don't understand what I'm supposed to do with y = 3x-1, substitute x = 2?

#### HallsofIvy

MHF Helper
Determine the equation of the tangent line to the graph of f(x) = -4x^2 + 11x - 2 at x = 2 that is parallel to the line y = 3x - 1.
Is that really what the problem says? If so, no wonder you are confused! That question, as stated, has no answer.

You know that the derivative of a function, at a given point, is the slope of the tangent line. The line y= 3x- 1 has slope 3 so any line parallel to that also has slope 3. So you want to find a point on the curve that has derivative 3:
f'(x)= -8x+ 11. At "x= 2" as you wrote, f'(2)= -16+ 11= 5, NOT 3. The tangent line at x= 2 is NOT parallel to y= 3x- 1.

However, it the problem said only "Determine the equation of the tangent line to the graph of f(x) = -4x^2 + 11x - 2 that is parallel to the line y = 3x - 1" without the "at x= 2" then it is quite doable. The slope of the tangent line is f'= -8x+ 11= 3 gives x= 1 (NOT 2). At x= 1 f(x)= -4+ 11- 2= 5 so the equation of the tangent line at x= 1 is y= 3(x- 1)+ 5= 3x+ 2.

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#### izzy0817

Yup I'm just gonna wait for my teacher to email me back. But that is exactly what the questions says (Worried)

#### izzy0817

So this is the response I got from my teacher:

I do not understand how I should solve Task 2, Question # 9.

Note: This is a question in the "thinking" part of the evaluation. These questions are designed specifically so that there is no direct example of how to do them. They are there to determine your problem solving skills.

As a result I cannot tell you exactly how to do any of these questions.
I can offer hints and suggestions.

Determine the equation of the tangent line to the graph of f(x) = -4x^2 + 11x - 2 at x = 2 that is parallel to the line y = 3x - 1.

What does parallel to line y = 3x - 1 mean?

Parallel lines have equal slopes.
The line y = 3x - 1 has slope 3

How do I apply the function to find the equation of the tangent line?
The slope of the tangent line is also the instantaneous rate of change of the function at a particular point. ( also known as the derivative )

#### izzy0817

still not sure what to do...(Crying)

#### Archie

This is the approach I outlined in my post above. If you use $$\displaystyle x=1$$ you will get a tangent as required, although your teacher may want you to use $$\displaystyle x=2$$ as stated. I'd write to your teacher and explain that the given line is not parallel to the tangent at $$\displaystyle x=2$$ and ask him what you should do about that.

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