Asked by lee
the point p is on the graph f(x)=x^2+2x+5 determine the distance from the point (-3,-2) to the point P as a function of x
Answers
Answered by
oobleck
If the point (h,k) is closest to P, then the distance is
z = √((h+3)^2 + (k+2)^2) = √((h+3)^2 + (h^2+2h+8)^2)
dz/dh=0 at h = -1.1533
f(-1.1533) = 4.0235
so P = (-1.1533,4.0235)
check:
the slope of f(x) is 2x+2
f'(-1.1533) = -0.3066
so the slope of the normal is -3.2626
and the slope of the line from P to (-3,-2) is
(4.0235+2)/(-1.1533+3) = 3.2618
close enough for me.
z = √((h+3)^2 + (k+2)^2) = √((h+3)^2 + (h^2+2h+8)^2)
dz/dh=0 at h = -1.1533
f(-1.1533) = 4.0235
so P = (-1.1533,4.0235)
check:
the slope of f(x) is 2x+2
f'(-1.1533) = -0.3066
so the slope of the normal is -3.2626
and the slope of the line from P to (-3,-2) is
(4.0235+2)/(-1.1533+3) = 3.2618
close enough for me.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.