Asked by Ally
For what values of c does the function f (x) = cx + arctan x have exactly one local maximum and one local minimum?
Answers
Answered by
oobleck
f'(x) = c + 1/(x^2+1) = (cx^2+x+c)/(1+x^2)
One max and one min means that cx^2 + x + c has two real roots, so
4-4c^2 > 0
c^2 < 1
Clearly, c>0 has no extrema, since both cx and arctanx are always increasing
So, -1 < c < 0
One max and one min means that cx^2 + x + c has two real roots, so
4-4c^2 > 0
c^2 < 1
Clearly, c>0 has no extrema, since both cx and arctanx are always increasing
So, -1 < c < 0
Answered by
ally
where does the 4-4c^2 come from
Answered by
oobleck
review the discriminant of a quadratic.
Think back to Algebra I
Think back to Algebra I
Answered by
ally
b^2 - 4ac? Where does the 4 come from, as well is the value of a 1?
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