# Math Help - differentiable function

1. ## differentiable function

If the function f(x) is differentiable

and

f(x) =
ax^3 - 6x ; x <= 1
bx^2 + 4 ; x > 1

then a =

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

2. Originally Posted by DINOCALC09
If the function f(x) is differentiable

and

f(x) =
ax^3 - 6x ; x <= 1
bx^2 + 4 ; x > 1

then a =

A) 0
B) 1
C) -14
D) -24
E) 26
As f is differentiable f'(x)=3ax-6 for x<=1 and 2b+4 for x>1.

But both f must be continuous so at x=1 we must have:

a-6 = b+4

and as it is differentiable at x=1 we must also have:

3a-6 = 2b+4

Now solve these simultaneous equations for a.

RonL

4. Originally Posted by DINOCALC09
If the function f(x) is differentiable
and

f(x) =
ax^3 - 6x ; x <= 1
bx^2 + 4 ; x > 1
Hello,

if f is differentiable at x = 1 you have to solve for a and b:

$\begin{array}{lcr}f(1)=g(1)&\text{that means}&a-6=b+4\\f'(1)=g'(1)&\text{that means} &3a-6=2b \end{array}$

which will yield a = -14 and b = -24