SAT Scores by Income The following graph shown U.S. math SAT scores as a function of parents’ income level. 81 Income ($1,000). The regression curve shown is given by f ( x ) = − 0.0034 x 2 + 1.2 x + 444 ( 10 ≤ x ≤ 180 ) where f ( x ) is the average math SAT score of a student whose parents earn x thousand dollars per year. Compute and interpret f ′ ( 30 ) .
SAT Scores by Income The following graph shown U.S. math SAT scores as a function of parents’ income level. 81 Income ($1,000). The regression curve shown is given by f ( x ) = − 0.0034 x 2 + 1.2 x + 444 ( 10 ≤ x ≤ 180 ) where f ( x ) is the average math SAT score of a student whose parents earn x thousand dollars per year. Compute and interpret f ′ ( 30 ) .
Solution Summary: The author analyzes the function f(x) and the graph which shows the U.S. math SAT scores as a function of parents income level.
SAT Scores by Income The following graph shown U.S. math SAT scores as a function of parents’ income level.81
Income ($1,000).
The regression curve shown is given by
f
(
x
)
=
−
0.0034
x
2
+
1.2
x
+
444
(
10
≤
x
≤
180
)
where
f
(
x
)
is the average math SAT score of a student whose parents earn x thousand dollars per year. Compute and interpret
f
′
(
30
)
.
Use Euler's method to numerically integrate
dy
dx
-2x+12x² - 20x +8.5
from x=0 to x=4 with a step size of 0.5. The initial condition at x=0 is y=1. Recall
that the exact solution is given by y = -0.5x+4x³- 10x² + 8.5x+1
Find an equation of the line tangent to the graph of f(x) = (5x-9)(x+4) at (2,6).
Find the point on the graph of the given function at which the slope of the tangent line is the given slope.
2
f(x)=8x²+4x-7; slope of the tangent line = -3
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