Derivative of 4(x^2)+2.

[Koke]

I am having a problem when starting this problem. Dumb me didn't pay close attention in class the day that my teacher taught this.

The problem is as follows:

"Use the deffinition of the derivative:
f(x ) - f(a)
lim ----------------
x->a x - a
to find the value of f'(a)=-2.
f(x)=4(x^2)+2"
I have already proved by the power rule and other deffinition of derivatives, that the derivative of this function is 8. But I don't know where to stick numbers and solve. If someone could help me with the first couple of steps, it would be greatly appriciated. Thanks in advance.

 

[tkhunny]

All that is required is an understanding of function notation and a little algebra. Why is this hard?

f(x) = 4x^2 + 2

f(a) = 4a^2 + 2

f(x) - f(a) = [4x^2 + 2]-[4a^2 + 2] = 4x^2 - 4a^2 = 4(x^2 - a^2)

Oh, it's too painful to do any more for you. If it is not yet obvious to you how to proceed, you should go see your teacher and apologize for not paying attention in class. Perhaps you can get an extra homework assignment to help you drill before the exam.

 

[galactus]

The derivative of \(\displaystyle 4x^{2}+2\)=8x, not 8.