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makvit [3.9K]
1 year ago
9

Find the derivative of f(x) = 2x^2 - 4x +3

Mathematics
1 answer:
ivolga24 [154]1 year ago
8 0

Explanation

2x^2-4x+3

When taking derivatives of polynomials, we primarily make use of the power rule.

Power rule.

\begin{gathered} f(x)=x^n \\ \text{then} \\ f^{\prime}(x)=nx^{n-1} \end{gathered}

also, the derivate of a sum is the sum of the derivates

hence

\begin{gathered} g(x)=f(x)+h(x)+\ldots z(x) \\ g^{\prime}(x)=f^{\prime}(x)+h^{\prime}(x)+\ldots.z^{\prime}(x) \end{gathered}

Step 1

apply:

\begin{gathered} f(x)=2x^2-4x+3 \\ f^{\prime}(x)=2\cdot2x^{2-1}-4(1)x^{1-1}+ \\ f^{\prime}(x)=4x^{}-4(1)x^0+3^0 \\ f^{\prime}(x)=4x^{}-4(1)(1) \\ f^{\prime}(x)=4z-4 \end{gathered}

therefore, the answer is

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Tammy and Lisa will make the same amount of money when they each sell 3 items. It'll probably never happen, though, since Tammy is a much better saleswoman than Lisa. You should hear her in action: "What will it take to put you in this foot spa today?" What a pro.

Now let's do the same problem in symbols. We need to find the two equations described by the problem.

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Lisa's line has a y-intercept of 10 and a slope of 3, so her equation is

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We've found a system of equations:

The problem asks how many items sold will give Tammy and Lisa the same amount of money, so we want to find x when the y-values on the two lines are the same. That is, we want to find where the lines intersect, which we can do by solving the system of equations. Why did one line cross the other line? To get to the other side. Oh...you've probably heard the version with the chicken.

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