Question #a681a

1 Answer
Mar 20, 2017

Answer:

The minimum value of the above is -1.5, which occurs when x = -1.5

Explanation:

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 * (-1.5)^2 + 6 * (-1.5) + 3 = 2 * 2.25 - 9 + 3 = 4.5 - 9 + 3 = -4.5 + 3 = -1.5#. Also, #d^2 f(x) / dx^2 =4#. Since this is positive, what we have calculated is the minimum value. If #d^2 f(x) / dx^2# had been negative, what we have calculated as per the above procedure is the maximum value of the function.