# Find $f'(a)$ of $f(x)$

What is $f'(a)$ of the function $f(x)$?

$$f(x) = 2x^2 − 3x + 1$$

I have been trying to do it but I cannot figure out how to do it. Please somebody can help me.

• Do you know how to calculate $f'(x)$? – Arthur Jan 25 '17 at 22:46
• Yes I do know, it is 4x-3 – David Romero Jan 25 '17 at 22:47
• Just replace x with a now. – randomgirl Jan 25 '17 at 22:49
• $f'(a) \to \left. {\frac{d}{{dx}}f(x)\,} \right|_{\,x\, = \,a}$ – G Cab Jan 25 '17 at 22:57
• – Jack Jan 26 '17 at 0:37

When we write $f'(x) = 4x-3$, that means that $x$ is a placeholder. In other words, exactly what symbol we use is of little consequence. Thus, we have, for instance, $$f'(\color{red}x) = 4\color{red}x-3\\ f'(\color{red}5) = 4\cdot \color{red}5 - 3\\ f'(\color{red}\dagger) = 4\color{red}\dagger - 3\\ f'(\color{red}わ) = 4\color{red}わ - 3$$ and, of course, $f'(\color{red}a) = 4\color{red}a - 3$.
The (almost) only time to be careful is when we insert specific numbers. See, we might have written $f'(5) = 17$, which is technically correct, but that makes it difficult to see exactly how the $5$ we insert affected the result. However, when using other symbols, like $a, x,$ etc., this is usually not a problem.
We have $$f'(x) = 4x - 3$$ by simply using that $$(x^n)' = nx^{n-1}$$ for any $n \in \mathbb{N}$. Then you just plug $a$ in for $x$, so $$f'(a) = 4a - 3$$