Question

Find an equation of the tangent line to the graph of f at the given point. f(x) = x^2 + 3, (1, 4)

Answer 1

Have you considered the 1st derivative, f'(x) evaluated at x = 1 to give the slope of this mysterious tangent line?

Answer 2

I don't know how to do this problem.

Answer 3

Have you heard of the 1st Derivative?

Answer 4

no

Answer 5

Is this a placement test?

Answer 6

no, homework. My teacher is foreign & hard to understand

Answer 7

What course is this? Is it Calculus I?

Answer 8

yes

Answer 9

if you can give me an equation, I can probably figure it out, just don't know what the (

Answer 10

Bear with me. Just trying to figure out where you are.

Have you been introduced to an odd-looking ratio, like this \(\dfrac{f(x+h) - f(x)}{h}\)?

Answer 11

sorry I lost you. I know that equation, just don't know what the (1,4) is for?

Answer 12

The very first thing to do is to verify that (1,4) is actually ON the curve. Is it?

Answer 13

I don't think so

Answer 14

not totally sure how to read the graphs either

Answer 15

f(x) = x^2 + 3

f(1) = 1^2 + 3 = 1+3 = 4

(1,4) is on f(x)

You ARE going to have to get better at some of these basic skills. This class is going to be a LONG HARD struggle if you don't remember anything from your prerequisites.

Algebra I
Algebra II
Geometry
Trigonometry
Hopefully Analytic Geometry
Hopefully "College Algebra"

We're going to need all the algebra and geometry skills we can get to survive just today. What do you think? Are you up to it?

Answer 16

I am. This is my last math class, so I do need to pass it. Thank you!

Answer 17

Okay, then... In the Differential Calculus, we have this amazing thing known as the 1st Derivative. It can be loosely defined as the slope of the tangent line at any given point on a curve (where it works, anyway). Our task is to define a little more carefully exactly what that means.

You may be familiar with a line tangent to a circle. It is a line that just touches the circle. There is only one point of intersection. If you hit the circle twice, it is a secant line.

How are we doing? Up to speed on these concepts?