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If the 2nd derivative of an equation isn't constant is it still a quadratic relation?
No. A quadratic equation always has a second derivative that is a constant. For example -3x2 + 10x - 2 first derivative -6x + 10 second derivative -6
What do you do if the second difference in a quadratic equation is 1?
The second difference of a quadratic equation being one indicates the second derivative at that point is positive. What you do from there depends on what property or transformation you're looking for with respect to the equation.
What is the double prime of 5x?
The "double prime", or second derivative of y = 5x, equals zero. The first derivative is 5, a constant. Since the derivative of any constant is zero, the derivative of 5 is zero.
Force divided by mass equals?
Newton's Second Law: force = mass x acceleration. Rearranging the equation, you see that force / mass = acceleration.
Is c equals ab to the second power a equation or expression?
It is an equation ... Anything with an equals is an equation 2+b=6 Anything without an equals is an expression 2+a
What is second order differential equation?
The highest order of derivative is 2. There will be a second derivative {f''(x) or d2y/dx} in the equation.
What is Y double-prime plus y equals 0?
y"+y'=0 is a differential equation and mean the first derivative plus the second derivative =0.Look at e-x the first derivative is -e-xThe second derivative will be e-xThe sum will be 0
If the 2nd derivative of an equation isn't constant is it still a quadratic relation?
No. A quadratic equation always has a second derivative that is a constant. For example -3x2 + 10x - 2 first derivative -6x + 10 second derivative -6
What is the difference between a first order and a second order differential equation?
A first order differential equation involves only the first derivative of the unknown function, while a second order differential equation involves the second derivative as well.
What do you do if the second difference in a quadratic equation is 1?
The second difference of a quadratic equation being one indicates the second derivative at that point is positive. What you do from there depends on what property or transformation you're looking for with respect to the equation.
What is the double prime of 5x?
The "double prime", or second derivative of y = 5x, equals zero. The first derivative is 5, a constant. Since the derivative of any constant is zero, the derivative of 5 is zero.
3rd derivative of y equals mx plus b?
The first derivative is m and the second is 0 so the third is also 0.
Force divided by mass equals?
Newton's Second Law: force = mass x acceleration. Rearranging the equation, you see that force / mass = acceleration.
Is c equals ab to the second power a equation or expression?
It is an equation ... Anything with an equals is an equation 2+b=6 Anything without an equals is an expression 2+a
What is y equals 7x plus 1?
y=7x+1 is a linear equation with a slope of 7 and y-intercept at (0,1). It contains two variables, y and x and cannot be solved unless one variable is given. The x-intercept to this equation is (-1/7,0). The first derivative of the equation would be y=7, a horizontal line with y-intercept (0,7). The second derivative and jerk cannot be taken.
At the maximum point the value of the second derivative of a function is?
At the maximum point of a function, the value of the second derivative is less than or equal to zero. Specifically, if the second derivative is negative, it indicates that the function is concave down at that point, confirming a local maximum. If the second derivative equals zero, further analysis is needed to determine the nature of the critical point, as it may be an inflection point or a higher-order maximum.
Can the concavity of a curve be determined by differentiation?
Yes, the concavity of a curve can be determined by differentiation. To find out the concavity of a graph at various points, you want to analyze the second derivative (f''(x)). Take the derivative of your original equation, then, take the derivative of this equation. By setting this second derivative to zero, you can solve for the critical points (x-intercepts/asymptotes) of the second derivative graph. Once these critical points are found, make a number line with these points marked. By doing a sign test on either sides of the critical points (plug in numbers below and above the critical points into the second derivative equation), you can find the concavities of your original graph. Wherever the sign tests results in a positive number, that is where a upward facing curve is (concave up); where it is negative, that is where a concave down portion is.
