Determine without graphing, whether the given function has a maximum value and then find the value. f(x)=3x^2+18x-6
since the x^2 term has a positive coefficient, there is no maximum value for f. As x gets large, so does f, without bound.
To determine if the given function has a maximum value without graphing, you can utilize calculus.
The function provided is f(x) = 3x^2 + 18x - 6. To find the maximum value, you need to find the vertex of the parabolic curve represented by the function.
The vertex of a parabola represented by a quadratic equation in the form of f(x) = ax^2 + bx + c, can be found using the formula x = -b / 2a. In this case, a = 3 and b = 18.
Substituting these values into the formula, we get x = -18 / (2 * 3) = -18 / 6 = -3.
To find the corresponding y-value (the maximum value), substitute the x-value (-3) back into the original function:
f(-3) = 3(-3)^2 + 18(-3) - 6
= 3(9) - 54 - 6
= 27 - 54 - 6
= -33
Therefore, the maximum value of the function f(x) = 3x^2 + 18x - 6 is -33.