Find the derivative function f' for the following functio...

Question

Find the derivative function f' for the following functions f.

f(x) = 2/3x+1; a= -1

Accepted Answer

Welcome back, everyone. In this problem, we want to calculate the derivative P for the function P X equals 95 X minus 4 at X equals 0. A says it's 0, B 9/5, C 95, and D 59. Now, if we're going to calculate the derivative for our function, OK, first, let's find the derivative and then evaluate it at our value at X equals 0. And to find the derivative, we can use the limit definition. Because by the limit definition, OK. What it basically tells us. Is that The derivative of our function in this case, the derivative of PF X will be equal to the limit as H approaches 0 of P X plus H. Minus p of X, all divided by H. So we'll just need to find P X + H, substitute P X, and then try to simplify it to figure out our derivative. Now what do we know? Well, we know that P X is 9/5 of X minus 4, OK? So this means then that the limit. As H approaches 0 of our expression, for a P X + H, we're going to substitute X + H into X into our function. So that's going to be 9/5 of X + H minus 4, OK, for P X plus H. Minus P X, which is 9/5 of X minus 4. I know all of this is going to be divided by H. Now if we go ahead and simplify here, OK, and that's gonna be the limit as it approaches 0. Of expanding our bracket 9/5 of X plus 9/5 of H minus 4 minus subtracting this entire expression, 9/5 of X plus 4. We subtract negative 4, it becomes positive 4. No, we can cancel like terms. 9/5 of X minus 9/5 of X is 0 and -4 + 4 is 0. And no, that leaves us with the limit as H approaches 0 of 9/5 of H divided by H. H cancers H that leaves us with the limit as H approaches 0 of 9/5, and we know that the limit of an expression as it approaches a constant equals the constant. In other words, this is going to be 9/5. Thus, P X, the derivative of P X is 9/5th. That means at X equals 0, OK. Then the derivative is still going to be 9/50 because it's a constant. Therefore, the derivative of payoff X at X equals 0 is 9/5. If we look back at our answer choices, that means C is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

Find the derivative function f' for the following functions f.
f(x) = 2/3x+1; a= -1

Key Concepts

Derivative

Power Rule

Constant Rule

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