What Are the Values of A and B to Make f Differentiable at 0?

[jason_r]

Use the definition of the derivative to determine all possoble values of A and B?
Use the definition of the derivative to determine all possoble values of A and B that make the function f differentiable at 0.


F(x)={ Ax^2 + Bx if -infin < x <= 0
{ x^3/2*cos(1/x) if 0<x<infin

I used defintion of derivative and equated both sides after i got both derivatives but i can't solve for the constants

any help

 

[lurflurf]

A and B need to be chosen so that
f(0-)=f(0)=f(0+)
f'(0-)=f'(0)=f'(0+)
what do you find for
f(0-)
f(0)
f(0+)
f'(0-)
f'(0)
f'(0+)
?

 

[lurflurf]

especially f'(0+)
are you sure the question is as written?

 

[jason_r]

especially f'(0+)
are you sure the question is as written?

yea the questoin is written correctly. This is part a: use differentiation formulas to find a formula for f''(x) for -infin<x<0 and 0<x<infin

and part b is the one i posted

 

[arildno]

" x^3/2*cos(1/x) if 0<x<infin"
I presume this should be read as:
$$x^{\frac{3}{2}}\cos(\frac{1}{x}), 0<x<\infty$$?

Take care to use the proper definition of the derivative at x=0..