Question

This is my question: Using the definition of the derivative at a point find f'(3) if f(x)=3x^3-2x^2+5.
(Hint synthetic division may be involved)

Answer 1

I'm not sure if this is right but:

Find the derivative by using differentiation:
f(x) = 3x^3-2x^2+5 (multiply the coefficient by the index and then subtract 1 from it)
f'(x) = (3*3)x^(3-1) - (2*2)x^(2-1) + 5x^(1-1)
f'(x) = 9x^2-4x

So now we can find f'(3):
f'(3) = 9*3^2-4*3
f'(3) = 81-12
f'(3) = 69

Therefore f'(3) = 69

Answer 2

thanks that looks right!