# Question #a681a

To find out the maximum or minimum, first differentiate the function with respect to x and equate it to 0. As you may know, the differential coefficient of a function represents the slope of the tangent of the function. So when the function reaches a maximum or minimum value, its slope is 0. That is the reason why we differentiate it and equate it to 0. In this case, df(x) / dx = 4x + 6. Equating this to 0, we get 4x + 6 = 0 or x = -1.5. Substituting it in the original function, we get f(-1.5) = $2 \cdot {\left(- 1.5\right)}^{2} + 6 \cdot \left(- 1.5\right) + 3 = 2 \cdot 2.25 - 9 + 3 = 4.5 - 9 + 3 = - 4.5 + 3 = - 1.5$. Also, ${d}^{2} f \frac{x}{\mathrm{dx}} ^ 2 = 4$. Since this is positive, what we have calculated is the minimum value. If ${d}^{2} f \frac{x}{\mathrm{dx}} ^ 2$ had been negative, what we have calculated as per the above procedure is the maximum value of the function.