(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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

2. Relevant equations

y = mx+b

f(1) = 4

f'(x) = (3x^2 + 1) / 2y

m = 1/2 when x = 1

3. 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 in to 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.

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

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