Question

If the function f(x) is differentiable and

f(x)=
{ax^3 + 6x, if x≤1
{bx^2 + 4, if x>1

then a =

What do I do?? No idea what's going on..

Answer 1

It must be continuous at x = 1
and
If it is differentiable at x=1, the slope must not change instantly at x = 1
in other words at x = 1:
A.
a x^3 + 6 x = b x^2 + 4
at x = 1
a+6 = b+4
or
a - b = -2
B.
3 a x^2 + 6 = 2 b x
at x = 1
a+6 = 2 b
or
a - 2 b = -6
There are two equations with two unknowns. Solve for a and b.

Answer 2

I GOT MY ANSWER IS B=4 AND A=2 IS IT RIGHT??

Answer 3

BUT MY MC ANSWERS FOR A IS NOT THERE...

A)0
B)1
C)-14
D)-24
E)26

WTF??

Answer 4

I get a = 2 also
check my arithmetic. I will as well.

Answer 5

3 a x^2 + 6 = 2 b x
at x = 1
3a+6 = 2 b
or
3a - 2 b = -6

Answer 6

Sorry, I get a = -2 and b = 0 however I look at it.

Answer 7

Put those values a = -2 and b = 0 back into the original equations and you find that they check. I think there is a typo in the problem statement.