Let f(x) = sin x. What is the value of f′(π)?

Question

Accepted Answer

Below there. Today we're going to 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. Evaluate F of X at X equals divided by 4 if F of X is equal to cosine of X. Awesome. So it appears our final answer that we're ultimately trying to solve for is we're trying to evaluate F of X at X equals pi divided by 4, if the original function is equal to cosine of X. So now that we know that we're trying to figure out the value for F of X at X equals pi divided by 4, let's read off our multiple choice answers to see what our final answer might be. A is 1/2, B is positive, the square root of 3 divided by 2, C is positive, the square root of 2 divided by 2, and D is negative square rooted 2 divided by 2. OK. So, first off, our first step that we need to take in order to solve this problem is we need to figure out the derivative. We need to find the derivative of F of X equals cosine of X. So we're trying to find the derivative of F of X is equal to cosine of X. So, essentially, we need to state that F of X, where this prime symbol denotes the first derivative, it looks like an apostrophe in the power. So F of X is going to be equal to negative sin of X, and that's when we take the derivative of cosine of X. Our second step that we need to take is we need to evaluate at X equals pi divided by 4. So we need to substitute the value X equals pi divided by 4. Into our derivatives. So we're trying to substitute this value in. So when we do that, we will find that F of pi divided by 4. It's going to be equal to negative sign of. I divided by 4, fantastic. And now our third step that we need to take is we need to calculate sign of pi divided by 4, and I need to take a moment here to pause, so let's pause here. So when we plug in sign of pi divided by 4 into our calculator, we need to make sure this is very, very important. You need to make sure your calculator is set to radiance mode. Because if your calculator is not in radiance mode, you will not receive the correct final answer. So make sure your calculator is not in degrees mode, make sure it's in radiance. So when you plug in sign of pi divided by 4. Into our calculator, you will receive an answer of the square root of 2 divided by 2 in radiance. Make sure once again your calculators in radiance mode, and then you'll get the square root of 2 divided by 2. So now we need to combine. So our fourth step is we need to combine. Or rather, we need to substitute in the sign of I divided by 4 equals the square root of 2 divided by 2 indoor calculation. So not, don't use the word combined, you need to you need to substitute our value of sign of pi divided by 4 equals the square rooted 2 divided by 2 into our expression. And when we do that, we will find that F of pi divided by 4 is equal to negative square rooted 2 divided by 2, and that is our final answer. Hooray, we did it. So therefore, the value of F of X at X equals pi divided by 4 is negative square rooted 2 divided by 2, and this corresponds to multiple choice answer letter D. So our final. Answer without a doubt will be multiple choice answer letter D, which once again is negative square rooted 2 divided by 2. Thank you so much for watching. Hopefully that helped, and I can't wait to see you in the next video. Bye.

Let f(x) = sin x. What is the value of f′(π)?

Key Concepts

Derivative

Trigonometric Functions

Value of f′(x) at Specific Points

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