Question

I REALLY need help with these derivative problems. I have done most of the work for 18 other problems, but do not understand how to solve these three. Can someone PLEASE help me? My work is due by midnight tonight.

Answer 1

b) `f(x)=5x^2-6x-3`

`lim_(hto0)(f(x+h)-f(x))/h=lim_(hto0)(5(x+h)^2-6(x+h)-3-5x^2+6x+3)/h=`

`=lim_(hto0)(5x^2+10hx+5h^2-6x-6h-3-5x^2+6x+3)/h=`

`lim_(hto0)(10hx+5h^2-6h)/h=lim_(hto0)10x+5h-6=10x-6`

The common factor is `h` and the polinomial is `10x+5h-6` and the expresion for `f´(x)=10x-6`

a) `f(x)=abs(3+9x)`

if `3+9x>=0` then `abs(3+9x)=3+9x`

But `3+9x>=0` its the same that `x>= -3/9=1/3`

Then if `x>=-1/3` we have `f(x)=3+9x`
If `x<-1/3`, then `f(x)=-3-9x`

We are ready to answer

If `x<-1/3` `f´(x)=-9`

Left hand derivative is -9
right hand derivative is 9

Thus, the derivative in `x=-1/3` does not exists

Sorry for last one...I cant see anything (too small)