equation of the tangent line to f(x) = 7x^2 at (4, f(4))

[marlalp]

Let me briefly explain my situation. I'm taking a course online and currently in the middle of a very long (so far 7 step) calculus problem that has taken all night so far. I get 3 guesses per step and on this last question, I'm down to one guess. If I get it wrong, I have to start all over again. Here is the problem:

What is the equation of the tangent line at (4, f(4)) for f(x) = 7x^2?

The problem I'm having is that the answer boxes the software gives are formatted like this:

y = [blank]x + [blank]

My answer (which must be wrong) is:

y = 56x - 112
or
y = x - 2

which is formatted like

y = [blank]x - [blank]

See the problem? Now can anyone PLEASE help me out here and tell me what I'm doing wrong? Thank you!!

 

[stapel]

See the problem?

Um... no...?

Now can anyone PLEASE help me out here and tell me what I'm doing wrong?

Since you haven't shown your steps or reasoning (so we don't know how you arrived at your two different answers), then no, I'm afraid we cannot tell you what you've done wrong -- or right. Sorry.

Eliz.

 

[marlalp]

The software used for my homework forces me to use two boxes to enter my answer:

y = [blank]x + [blank]

Note the plus sign.

The answer I arrived at:

y = 56x - 112

Has a minus sign. That is my problem.

Here are the steps I used:


f'(x)=2*7x
f'(4)=2*7*4=56
the point where the tangent line touches f(x) is
f(4)=7(4)^2=112 --> (4,112)

using the formula y=mx+b
112=56(4)+b
solve for b= - 112
answer: y = 56x - 112

 

[galactus]

Your answer is correct.

 

[stapel]

The software used for my homework forces me to use two boxes to enter my answer... [with a] plus sign.....The answer I arrived at...Has a minus sign. That is my problem.

Why would that be a problem? Hasn't your class covered "integers" and integer arithmetic? They should have covered how, for instance, "1 - 2" is the exact same thing as "1 + (-2)". If not, you might want to do some review. A tutor should be able to cover this material with you (that is, working with you in person, face to face) in only a few hours.

Eliz.