Answer:
the linearization is y = 1/4x +5/4
the linearization will produce <em>overestimates</em>
the values computed from this linearization are ...
f(3.98) ≈ 2.245
f(4.05) ≈ 2.2625
Step-by-step explanation:
Apparently, you have ...

from which you have correctly determined that ...

so that f(3) = 2 and f'(3) = 1/4. Putting these values into the point-slope form of the equation of a line, we get the linearization ...
g(x) = (1/4)(x -3) +2
g(x) = (1/4)x +5/4
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The values from this linearization will be overestimates, as the curve f(x) is concave downward everywhere. The tangent (linearization) is necessarily above the curve everywhere.
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At the given values, we find ...
g(3.98) = 2.245
g(4.05) = 2.2625
The passenger travelled 12 miles
There is 15 bars in each case.
Subtract 8 from 143 and you get 135.
Divide 135 by 9 and you get 15 :)
For the answer to the question above, this is a right triangle problem using the tangent function.
<span>Tan(x) = Opposite (O) / Adjacent (A) </span>
<span>x = 40 degrees </span>
<span>A = 30 ft </span>
<span>Solve for O </span>
<span>O= Tan (x) * A </span>
<span>O = Tan (40) * 30 </span>
<span>Use your calculator or whatever method to get the tangent of 40 degrees (which is .84) </span>
<span>O = .84 * 30 </span>
<span>O = 25.2 Ft</span>
The answer should be 6.34. This is because since the 6 is in the ones place, it should be the whole number. The 3 is a tenths so it should be the first number after the decimal. Finally, since 4 is in the hundredths place, it should be two places from the whole number.