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(s) = 4s³+3s; a= -3, -1

Accepted Answer

Welcome back, everyone. Given the function P of Y equals 6 Y cubed plus Y, evaluate P D for D equals -5 and D equals 1. A says P-5 equals 151, while P 1 equals 7. B says they are 151 and 19. C 451 and 7, and D, 451 and 19. Now, if we're going to evaluate P D, OK, first, we need to figure out the derivative of P of Y. So let's find the derivative of P Y P Y, and then we can go ahead and solve for P D for our varying values of D. That is when it's -5 and when it's 1. No given P F Y. OK. Being equal to 6 YQ plus y. If we were to differentiate here, we can differentiate both terms using the power rule. Recall that by the poor rule of differentiation, it tells us that the derivative of a term that's raised to our power is going to be equal to or power n multiplied by x to the power of n minus 1. In other words, we bring down the power and then subtract 1 from the power in the original term. Applying the power rule of differentiation here, this tells us that the derivative of p of y. Is going to be equal to 3 multiplied by 6 Y squared, OK, plus 1 multiplied by Y raised to the pore of +01 minus 1, OK? Because here for why we can assume the poor is one. Now, in that case, 3 multiplied by 6 Y squared is 18 Y2 and Y 1 minus 1 is Y 0, which is 1. So here we're gonna have 18 Y2 + 1 as the derivative of P Y. Now that we have this expression, we can go ahead and solve for P D where D is -5 and D is 1. When D equals -5. OK, then that means P-5 is going to be equal. The 18 multiplied by -5 2 + 1. Now we know Well, let me write it below it here. OK, let me, let me make some space actually. Now we know that -5 squared is gonna be 25, so that's 18 multiplied by 25 + 1 and 18 multiplied by 25 is 450. So this is 450 plus 1, which equals 451. So P of -5 is 451. Next, let's try to figure it out when D equals 1, OK? Know when D equals 1. OK. Then P1 is going to be equal to 18 multiplied by 1 squared plus 1. 1 squared is 1 and 18 + 1 equals 19. Therefore, P 1 is equal to 19. Thus when D equals -5, P-5 is 451, and when D E equals 1, P 1 E equals 90. If we look back at our answer choices, that tells us D is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

21–30. Derivatives
b. Evaluate f'(a) for the given values of a.
f(s) = 4s³+3s; a= -3, -1

Key Concepts

Derivatives

Power Rule

Evaluating Derivatives at Specific Points

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