Equation for the line tangent to the graph and use it to approx. f(1.2)

[lude1]

Homework Statement

Write an equation for the line tangent to the graph of f at x = 1 and use it to approximate f(2.1).

Homework Equations

y = mx+b
f(1) = 4
f'(x) = (3x^2 + 1) / 2y
m = 1/2 when x = 1

The Attempt at a Solution

Well, if the line is tangent to the graph of f at x = 1, that means they have the same slope (I think). Thus,

y = (1/2)x + b​

I have the point (1, 4) so I plug that into find b

4 = (1/2)(1) + b
b = 8​

Thus, I have

y = (1/2)x + 8​

Since they want me to approximate f(2.1), I would plug in 2.1 for x and solve for y. But, my answer is wrong. The correct answer is

y - 4 = (1/2)(x-1)
f(1.2) = 4.1​

My equation is wrong (and thus my answer), which leads me to believe that I'm approaching this incorrectly.

 

[The Chaz]

4 = (1/2)(1) + b
b = 8
...
That's wrong. b = 3.5

 

[lude1]

Oh my gosh, I can't believe I did that wrong even after I checked it over a few times!

Thanks!

 

[The Chaz]

You wouldn't believe some of the mistakes I've made.
e.g. In a state competition, I calculated 98 - 64 = 32. We lost by a point.