What is the difference between 89.4 and 13.621? Do not round your answer.
2 answers:
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Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Calculate m using the slope formula
m =
with (x₁, y₁ ) = (0, 3) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = =
= -
The y- intercept is where the line crosses the y- axis
The line crosses the y- axis at (0, 3 ) ⇒ b = 3
(b)
y = - x + 3 ← equation of line
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
