Find the first four iterates of the function f(x) = (x - 5)2 with an initial value of x0 = 4.
1 answer:
Answer:
b. 1; 16; 121; 13,456
Step-by-step explanation:
A suitable calculator or spreadsheet can compute these for you.
Put the value of x into the formula to find the first iterate. Repeat for successive iterates.
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<em>Comment on the answer choices</em>
You can eliminate the first two answer choices because none of the numbers 19, 645, 12645 are perfect squares. You can eliminate the last answer choice because the first term listed is x0, not x1.
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Answer:
(a) f'(1)=-4
(b) y+4x-4=0
Step-by-step explanation:
<u>Tangent Line of a Function</u>
Given f(x) a real differentiable function in x=a, the slope of the tangent line of the function in x=a is given by f'(x=a). Where f' is the first derivative of f.
We are given
The derivative is
(a) The slope of the tangent line at (1,0) is
(b) The equation of the tangent line can be found with the general formula of the line:
Where m is the slope and the point (xo,yo) belongs to the line. We have m=-4, xo=1, yo=0, thus
Or, equivalently