Mathematics, 15.07.2020 03:01 19thomasar
Suppose that we don't have a formula for g(x) but we know that g(3) = −1 and g'(x) = x2 + 7 for all x.
(a) Use a linear approximation to estimate g(2.95) and g(3.05).
g(2.95) =
g(3.05) =
(b) Are your estimates in part (a) too large or too small? Explain.
A) The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie below the curve. Thus, the estimates are too small.
B) The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie below the curve. Thus, the estimates are too small.
C) The slopes of the tangent lines are positive and the tangents are getting steeper, so the tangent lines lie above the curve. Thus, the estimates are too large.
D) The slopes of the tangent lines are positive but the tangents are becoming less steep, so the tangent lines lie above the curve. Thus, the estimates are too large.
Answers: 3
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Imogene invested $8,000 in a bank account that pays 8 percent simple interest at the end of each year. her friend invested the same amount in stocks where the growth of the investment is represented as 2,000 times the square root of 2 less than the time lapsed in years. if y1 and y2 represent the amount earned in dollars and t is the time lapsed in years, which system of equations correctly represents the situation?
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Suppose that we don't have a formula for g(x) but we know that g(3) = −1 and g'(x) = x2 + 7 for all...
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