y = - 6x2 - 12x - 1 A second degree equation graphs as a parabola, and has only one max or min. At that point, the first derivative y' = 0. dy/dx = - 12x - 12 = 0 - x - 1 = 0 ==> x = - 1 At that point, y = - 6( 1 ) - 12( - 1 ) - 1 = - 6 + 12 - 1 = 5. The max value of the function is 5, and occurs when x = -1.
When you solve for the 2nd derivative, you are determining whether the function is concave up/down. If you calculated that the 2nd derivative is negative, the function is concave down, which means you have a relative/absolute maximum, given that the 1st derivative equals 0. To understand why this is, think about the definition of the 2nd derivative. It is a measure of the rate of change of the gradient. At a maximum, the gradient starts positive, becomes 0 at the maximum itself and then becomes negative, so it is decreasing. If the gradient is going down, then its rate of change, the 2nd derivative, must be negative.
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The [ 2x + 1 ] represents a function of 'y' .
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The question is not clear. A function is defined by an equation and that requires an equals sign. there is no equals sign in the question. It is therefore impossible to give a proper answer to your question. Please resubmit your question spelling out the symbols as "plus", "minus", "times", "divided by", "equals".
The answer will depend on the ranges for x and y. If the ranges are not restricted, then C can have any value.
147 equals Maximum Break in Snooker.
yes. it is a function
determine whether each relation is a function y equals -8
volts divided by resistance equals maximum amperage (current)
exactly...
no
The condition for maximum velocity is acceleration equals zero; dv/dt = a= o.
Y = -0.02 d2 + 0.04 d + 1The function is maximum where its first derivative is zero.0 = -0.04 d + 0.04d = 1Y = -0.02 + 0.04Y = + 0.02That's the maximum value of the function given in the question. If we knew howthat function relates to the height of a frisbee, we might be able to provide anactual answer to the question.
The maximum value of the sine function is 1 and that the smallest value for a would be pie divided by 2. So, if 2a= pie divided by 2, then the answer is a=pie divided by 4(simply divide both sides by 2).
14.