Find the Critical Points y=2.3+3.4x-1.2x^2

Problem

y=2.3+3.4*x−1.2*x2

Solution

1. Find the derivative of the function with respect to x to determine the rate of change.

d(y)/d(x)=d(2.3+3.4*x−1.2*x2)/d(x)

2. Apply the power rule to each term of the expression.

d(y)/d(x)=3.4−2.4*x

3. Set the derivative to zero because critical points occur where the first derivative is zero or undefined.

3.4−2.4*x=0

4. Solve for x by isolating the variable on one side of the equation.

−2.4*x=−3.4

5. Divide both sides by −2.4 to find the value of x

x=(−3.4)/(−2.4)

6. Simplify the fraction to its decimal form.

x≈1.41666666667

Final Answer

x=17/12

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