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Problem 31 Medium Difficulty

Find $ f'(a) $.

$ f(x) = 3x^2 - 4x + 1 $

Answer

$6 a-4$

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Video Transcript

Okay in this problem we have F of X equals three X squared minus four X plus one. Uh Have prime of X. Taking the derivative of our function F. A bex the derivative of three X squared, while the derivative of X squared would be two times X to the first. Uh Such derivative of three X squared will be two times three X to the first or six X to the first or 6 6. So two times three X six X. And then we should attract one from that exponent. So it's X to the first, which we don't have to write to do and then bring down the subtraction. Sign. The derivative of four times X is just four and uh the derivative of a constant is zero. So we don't have to write plus zero. So here's F prime of X. Uh So if we want to find what is the derivative of F evaluated when X is a. We simply just plug a into the derivative function. So F prime of X is six times X minus four. F prime of a is six times a minus four.