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How do you trace a curve in differential calculus?
To trace a curve using differential calculus, you use the fact that the first derivative of the function is the slope of the curve, and the second derivative is the slope of the first derivative. What this means is that the zeros (roots) of the first derivative give the extrema (max or min) or an inflection point of the function. Evaluating the first derivative function at either side of the zero will tell you whether it is a min/max or inflection point (i.e. if the first derivative is negative on the left of the zero and positive on the right, then the curve has a negative slope, then a min, then a positive slope). The second derivative will tell you if the curve is concave up or concave down by evaluating if the second derivative function is positive or negative before and after extrema.
Why is negative 3 times 4 squared -48?
Order of operation is key. Square first. 4 squared is 16. then multiply 16x-3= -48. A negative times a positive is a negative.
How do you factor the expression two m squared minus eight?
2m^2 - 8 -First you should factor out a two. --> 2(m^2-4) -You now have something squared minus something else squared; You have m squared minus 2 squared. Whenever you have something squared minus something squared as you do in this case, there is a simple rule to remember: You can reduce that expression into the quantity of the square root of the first number or variable plus the square root of the second number or variable Times the quantity of the square root of the first number or variable minus the second number or variable squared. --> In the case of your expression: ----> 2(m+2)(m-2)<-----
How do you solve 2 times negative four squared?
first, you square negative 4. Since negative times negative is positive, then you get positive sixteen., Then positive 16 times two is 32
4.5cm x 3.5cm squared?
There are no parentheses so the order or operations, PEMDAS, means we do exponent first and square the 3.5. So 3.5 squared is 12.25 and now multiply by 4.5 and you have 55.125.If you mean square the quantity, (4.5x3.5) then the answer is different. First we have 4.5x3.5 is 15.75. Now 15.75 squared is3038.77.
What is the answer to the problem X cubed plus six x squared plus three x plus one divided by x minus two?
Your answer will depend on the parameters of the instructions. If you're looking for the first derivative, simply use the product rule by changing the denominator to a negative exponent and bringing it up (take the negative square root of the quantity x-2 to the top). Then, follow the rules of calculus and algebra. Wow, that's a mess. Let's see... you get "the quantity x cubed plus 6x squared plus 3x plus 1 times the quantity -1(x-2) raised to the negative second plus the quantity x-2 raised to the negative first times the quantity 3x squared plus 12x plus 3." This is because of the Product Rule. Simplifying (by factoring out (x-2) raised to the negative second and combining like terms) gives us "(x-2) raised to the negative second times the quantity 2x cubed minus 24x minus 7." This can also be written as "2x cubed minus 24x minus 7 all over the quantity x-2 squared." f'(x)= 2x^3-24x-7 (x-2)^2
Why are brackets needed to square negative numbers?
If you were to do -92, following the order of operations, exponents come before subtraction. Because of this -92 = -(92) which is -81. The quantity negative nine, squared, however is positive 81. In order to show that you want the entire quantity negative nine squared, you must use parenthesis (or brackets): (-9)2 = 81. This shows to do the "subtraction" first.
How do you trace a curve in differential calculus?
To trace a curve using differential calculus, you use the fact that the first derivative of the function is the slope of the curve, and the second derivative is the slope of the first derivative. What this means is that the zeros (roots) of the first derivative give the extrema (max or min) or an inflection point of the function. Evaluating the first derivative function at either side of the zero will tell you whether it is a min/max or inflection point (i.e. if the first derivative is negative on the left of the zero and positive on the right, then the curve has a negative slope, then a min, then a positive slope). The second derivative will tell you if the curve is concave up or concave down by evaluating if the second derivative function is positive or negative before and after extrema.
Why is negative 3 times 4 squared -48?
Order of operation is key. Square first. 4 squared is 16. then multiply 16x-3= -48. A negative times a positive is a negative.
How do you factor the expression two m squared minus eight?
2m^2 - 8 -First you should factor out a two. --> 2(m^2-4) -You now have something squared minus something else squared; You have m squared minus 2 squared. Whenever you have something squared minus something squared as you do in this case, there is a simple rule to remember: You can reduce that expression into the quantity of the square root of the first number or variable plus the square root of the second number or variable Times the quantity of the square root of the first number or variable minus the second number or variable squared. --> In the case of your expression: ----> 2(m+2)(m-2)<-----
How do you solve 2 times negative four squared?
first, you square negative 4. Since negative times negative is positive, then you get positive sixteen., Then positive 16 times two is 32
4.5cm x 3.5cm squared?
There are no parentheses so the order or operations, PEMDAS, means we do exponent first and square the 3.5. So 3.5 squared is 12.25 and now multiply by 4.5 and you have 55.125.If you mean square the quantity, (4.5x3.5) then the answer is different. First we have 4.5x3.5 is 15.75. Now 15.75 squared is3038.77.
What is the first derivative used for?
The first derivative f'(x) gives the instantaneous slope of f(x). If f'(x) is positive, then f(x) is increasing (positive slope), and if f'(x) is negative, then f(x) is decreasing (negative slope). If f'(x) = 0, then the graph of f(x) is flat at the point (slope = 0).
What is the scientifical definition for force?
Force is the pressure of something against another object.
How does a change in one quantity affect the change in other quantities?
Feedback in general is the process in which changing one quantity changes a second quantity, and the change in the second quantity in turn changes the first.Positive feedback amplifies the change in the first quantity while negative feedback reduces it.....
How do you find second derivative of a function?
All it means to take the second derivative is to take the derivative of a function twice. For example, say you start with the function y=x2+2x The first derivative would be 2x+2 But when you take the derivative the first derivative you get the second derivative which would be 2
What is the third derivative of lnx?
Oh, dude, the third derivative of ln(x) is -2/(x^3). But like, who really needs to know that, right? I mean, unless you're planning on impressing your calculus teacher or something. Just remember, math is like a puzzle, except no one actually wants to put it together.
