Question

Could someone provide me the steps to find this answer?
Find f '(a).
f(x) = 4x2 − 4x + 3

Answer 1

My understanding is I should take the derivatives for f(x).
(d/dx) (4x^2 - 4x +3)
4*(d/dx)[x^2] - 4*d/dx[x] + d/dx [3]
4*2x-4*1+0
8x-4

Answer 2

Yes,

\(\color{#000000 }{ \displaystyle f'(x)=8x-4 }\)

Answer 3

\(\color{#000000 }{ \displaystyle f'(a) }\) just means,

"the derivative (or, \(\color{#000000 }{ \displaystyle f'(x) }\)) evaluated at \(\color{#000000 }{ \displaystyle x=a }\).

Answer 4

Or, as far as the slope is concerned,

\(\color{#000000 }{ \displaystyle f'(a) }\) gives you the instantaneous slope of the function \(\color{#000000 }{ \displaystyle f(x) }\) at \(\color{#000000 }{ \displaystyle x=a }\).

Answer 5

if you have any questions, ask.

Answer 6

I will put up another example, just in case..

Answer 7

Luke, may the power rule be with you

but yours is correct Juscallmesteve

Answer 8

\(\color{#0aa000 }{ \displaystyle\bf Problem: }\)
\(\color{#000000 }{ \displaystyle f(x)=2x^3-5x^2+5x+3 }\). Find, \(\color{#000000 }{ \displaystyle f'(7) }\).

\(\color{#0aa000 }{ \displaystyle\bf Solution: }\)
\(\color{#000000 }{ \displaystyle f(x)=2x^3-5x^2+5x+3 }\) \(\tiny \\[0.6em]\)
\(\color{#000000 }{ \displaystyle f'(x)=(3-\color{red}{1})2x^{3-\color{red}{1}}-(2-\color{red}{1})5x^{2-\color{red}{1}}+5+0 }\) \(\tiny \\[0.6em]\)
\(\color{#000000 }{ \displaystyle f'(x)=(2)2x^{2}-(1)5x^{1}+5 }\) \(\tiny \\[0.6em]\)
\(\color{#000000 }{ \displaystyle f'(x)=4x^{2}-5x+5 }\) \(\tiny \\[0.6em]\)
\(\color{#000000 }{ \displaystyle f'(\color{blue}{7})=4\color{blue}{(7)}^{2}-5\color{blue}{(7)}+5 }\) \(\tiny \\[0.6em]\)
\(\color{#000000 }{ \displaystyle f'(\color{blue}{7})=4\cdot 49-35+5 }\) \(\tiny \\[0.6em]\)
\(\color{#000000 }{ \displaystyle f'(\color{blue}{7})=166 }\)