21–30. Derivatives
b. Evaluate f'(a) for the given ...

Question

21–30. Derivatives

b. Evaluate f'(a) for the given values of a.

f(x) = 4x²+1; a= 2,4

Accepted Answer

Hello there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. Determine the derivative of the function H of X is equal to 5 x 2 minus 2. And H of C or C equals -1 and C equals 2. Awesome. So it appears for this particular prompt, we're asked to solve for three separate answers. Our first answer is we're trying to figure out the derivative of the function H of X. And we're trying to solve for our second answer, which is H of C, where our first answers for C equals -1, that's technically our second answer, and then our third answer is for H of C where C equals 2. So once again to reiterate, we're ultimately trying to solve for three separate answers. Our first answers are trying to figure out what the derivative of H of X is for the function H of X, and that's our first answer. Our second answer is we're trying to figure out H C where C equals -1. That's our second answer. And our third answer is we're trying to figure out what H C is for when C equals 2. So with that said, first off, we need to once again reiterate that we're trying to find the derivative of the function. H X is equal to 5 x 2 minus 2, and now that we know that we're trying to differentiate H of X is equal to 5 x 2 minus 2, in order to differentiate this specific function, we need to recall and use the power rule for differentiation. And as we should recall, the power rule states that D by DX. Of X to the power of N. is equal to N multiplied by X to the power of N minus 1. So now what we need to do is we need to recall and apply the power rule to each term in our function, so we could therefore write that H of X is equal to D by DX of. 5 X to the power of 2 minus D by DX of 2. Fantastic. And now, our next step. we need to apply the differentiation, and when we do, we will get that H of X is equal to 5 multiplied by 2 X so the power 2 minus 1. 0, which will mean when we simplify that H of X is equal to 10 X, and that is our first answer. Hooray, we did it. So now, our next step is we need to solve for our second answer, which is H. Of C, and this is for the condition where C equals -1. So all we need to do is we need to substitute in the value for C equals -1 into our derivative of H. So when we do that, we will find that H. Of -1. It's going to be equal to 10, multiplied by -1, which will give us -10. Awesome, and that is our second answer, so this is for H of -1. Fantastic. And once again, our second answer is -10. And similarly, we're gonna need to solve for H of C where C equals 2, so plugging in 2 N for See, we will get that H2 is equal to 10 multiplied by 2, which will give us 20, which is our second or, sorry, that is our third answer. Hooray, we did it, and this is equal to H2, and that's it. We've solved for all three answers. Hooray, we did it. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

21–30. Derivatives
b. Evaluate f'(a) for the given values of a.
f(x) = 4x²+1; a= 2,4

Key Concepts

Derivatives

Power Rule

Evaluating Derivatives at Specific Points

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