Find the solution of the equation given below.7+(-5x) = -33
1 answer:
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a. Note that is continuous for all
. If
attains a maximum at
, then
. Compute the derivative of
.
Evaluate this at and solve for
.
To ensure that a maximum is reached for this value of , we need to check the sign of the second derivative at this critical point.
The second derivative at is negative, which indicate the function is concave downward, which in turn means that
is indeed a (local) maximum.
b. When , we have derivatives
Inflection points can occur where the second derivative vanishes.
Then we have three possible inflection points when ,
, or
.
To decide which are actually inflection points, check the sign of in each of the intervals
,
,
, and
. It's enough to check the sign of any test value of
from each interval.
The sign of changes to either side of
and
, but not
. This means only
and
are inflection points.
We can start by rewriting the initial equation <span>x +10y=260 in order to express how y depends on x.
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This is a linear function ( it's a straight line). Linear functions have two intercepts, y and x.
To find x-intercept (also called zero of a function) we set y=0 and we solve for x.
This means that at x=260 our function has a value of 0. y(x) represents a distance from the school. This means that when y(x) is 0 our athlete reached school (finished the race), so this also answers your second question. The time it takes an athlete to finish the race is 260 minutes.
The y-intercept a value of our function at x=0. This gives us a distance of our athlete from the school at the start of the race. We find this by plugin x=0 in our equation. We get that y=26 when x=0. This makes perfect sense. Our athlete is 26 miles away from high school at the start of the race.
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This is a linear function ( it's a straight line). Linear functions have two intercepts, y and x.
To find x-intercept (also called zero of a function) we set y=0 and we solve for x.
This means that at x=260 our function has a value of 0. y(x) represents a distance from the school. This means that when y(x) is 0 our athlete reached school (finished the race), so this also answers your second question. The time it takes an athlete to finish the race is 260 minutes.
The y-intercept a value of our function at x=0. This gives us a distance of our athlete from the school at the start of the race. We find this by plugin x=0 in our equation. We get that y=26 when x=0. This makes perfect sense. Our athlete is 26 miles away from high school at the start of the race.
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