y = -6x2 - 12x - 1
We recognize this as the equation of a parabola opening downward, but we don't need to know that in order to answer the question.
At the extremes of a function (local max or min), the first derivative of the function = zero.
The first derivative of the given function with respect to 'x' is dy/dx = -12x -12
Set -12x - 12 = 0.
-x - 1 = 0
x = -1
y = -6x2 - 12x - 1 = -6(1) - 12(-1) - 1 = -6 + 12 - 1 = 5
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In Calculus, to find the maximum and minimum value, you first take the derivative of the function then find the zeroes or the roots of it. Once you have the roots, you can just simply plug in the x value to the original function where y is the maximum or minimum value. To know if its a maximum or minimum value, simply do your number line to check. the x and y are now your max/min points/ coordinates.
No, this is not a function. The graph would have a vertical line at x=-14. Since there are more than one y value for every given x value, the equation does not represent a function. The slope of the equation also does not exist.
y = 5x + 3When x=2,y = 5(2) + 3 = 10 + 3 = 13
f(x) = 2 cos 3x The amplitude: A = |2| = 2 The maximum value of the function: 2 The minimum value of the function: -2 The range: [-2, 2]
maximum value of 6y+10y