- #1
lude1
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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
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
f(1.2) = 4.1
My equation is wrong (and thus my answer), which leads me to believe that I'm approaching this incorrectly.