The function is a peacewise function where 2kx^2 has a domain of x>3 and x^3+cx has a domain of x<= 3

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

We need to establish continuity at x=3.

So 2kx²-x=x³+cx so 18k-3=27+3c, 18k-3c=30, 6k-c=10, so c=6k-10

The gradients must also be the same at x=3, so

4kx-1=3x²+c at x=3, 12k-1=27+c, 12k-c=28, so c=12k-28.

Therefore 12k-28=6k-10, 6k=18, k=3 and c=8.

Now we have continuity and differentiability.

by Top Rated User (640k points)

Related questions

0 answers
0 answers
1 answer
asked Dec 13, 2012 in Pre-Algebra Answers by anonymous | 897 views
1 answer
1 answer
asked Jan 30, 2012 in Calculus Answers by anonymous | 193 views
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
82,854 questions
87,444 answers
3,925 users