The equation of the tangent line at x=1 can be written in point-slope form as
... L(x) = f'(1)(x -1) +f(1)
The derivative is ...
... f'(x) = 4x^3 +4x
so the slope of the tangent line is f'(1) = 4+4 = 8.
The value of the function at x=1 is
... f(1) = 1^4 +2·1^2 = 3
So, your linearization is ...
... L(x) = 8(x -1) +3
or
... L(x) = 8x -5
I have to see if you can get it done before the first day of the shower
P=42 m
1/2 of P=21
1/2 of P= l+w
21=13+8
A=13×8
A=104 m^2. As a result, the length is 13 m, and the width is 8 m. Hope it help!
2x + y = 5
x − 2y = 10
y = 5 − 2x
x − 2(5 − 2x) = 10
x − 10 + 4x = 10
5x − 10 = 10
<em>add 10 to each side</em>
<em>5x-10+10 = 10 + 10</em>
<em>5x=20</em>
5x = 0 <em>this is the error</em>
He needs to add 10 to each side