How many positive integers a (<1000) are there such that the function
f(x)=x^4−76/3x^3+2ax^2
has no local maxima?
4 answers
done giving you freebies. I'll be happy to check your work or point you in the right direction. You must have some idea how to solve such problems.
alright, so i got that
f'(x)=4x^3-76x^2+4ax
=4x(x^2-19x+4a)
since this must never equal 0, it must have no solutions. Therefore, x must not be 0 and x^2-19x+4a must not be 0. For that to occur, 289-16a<0, so a > 18.0625.
Can you please check me work?
Sorry for bothering you so much.
f'(x)=4x^3-76x^2+4ax
=4x(x^2-19x+4a)
since this must never equal 0, it must have no solutions. Therefore, x must not be 0 and x^2-19x+4a must not be 0. For that to occur, 289-16a<0, so a > 18.0625.
Can you please check me work?
Sorry for bothering you so much.
watch the algebra!
f'(x)=4x^3-76x^2+4ax
= 4x(x^2-19x+a)
The discriminant 361-4a must be negative, so a > 361/4
You could have seen that your answer was incorrect by graphing the resultant polynomial.
f'(x)=4x^3-76x^2+4ax
= 4x(x^2-19x+a)
The discriminant 361-4a must be negative, so a > 361/4
You could have seen that your answer was incorrect by graphing the resultant polynomial.
oops! Thanks for the help
1 answer