Wednesday, April 28, 2021

How To Simplify Difference Quotient?

zack April 28, 2021 No comments

f(a + h) − f(a) h =.The Difference Quotient is an algebraic approach to the Derivative ( dy ) and is sometimes referred to as the dx. "Four Step Method." It is a way to find the The idea of a limit is to get very close to a given value of (x) in f(x), even if f(x) is not defined at (x) and so in our equation, h→0 (h approaches zero)...Find and simplify the diﬀerence quotient for the given function. f(x)= -x^2+2x-1 I need The revenue in dollars from the sale of concert tickets at x dollars each is given by the function R(x)=46,400x-800x^2. Find the difference quotient when x=27 a h=0.1, and when x=31and h=o.1. Intepret your answers.The Difference Quotient This video gives the formula for the difference quotient (the subtraction fraction) and do a couple examples of finding it for different functions. Examples: a) Let f(x) = 2x - 5; find f(x+h) - f(x) b) Let f(x) = 3x + 2; find the difference quotient: (f(x+h) - f(x))/h.Transcribed Image Text from this Question. Find fa), fa +h), and the difference quotient t fia + h)-f(a), where h # 0. re rx) = 5-6x+9x2 f(a) = fta + h) = a + h)

PDF Difference Quotient

Learn more. Find $f(a)$, $f(a + h)$, and the difference quotient, given $f(x)=7-8x+2x^2$. Ask Question. I tried plugging everything in and simplifying to a point where my final answer was $(-8h+2ah+2h^2)/h$.Evaluate the difference quotient for the given function. For the function f(x) = 4 + 3x - x^2, determine (f(3+h) - f(3))/h and simplify the result.The quotient of these changes is a difference quotient for the function f; this difference quotient measures the average rate of change of y with respect to x on the interval [a , a + h ].def difference_quotient(f, x, h): return (f(x + h) - f(x)) / h. I understand that this is just the equation for finding the limit, and in this case the derivative, but I don't see how the script works. What arguments would you put into the function that would allow for a return statement of f(something) and not f...

Find f(a), f(a + h), and the difference quotient...

You can put this solution on YOUR website! f(x) = 5x^2 + 9 - f(a+h) = 5(a+h)^2+9 = 5[a^2+2ha+h^2]+9 = 5a^2+10ha+5h^2+9Find the difference quotient of f; that is , find f(x+h)-f(x)/h, h=0, for function: f(x)=x^2+5x-1… read more. abozer. Bachelor's Degree. 6,158 satisfied customers.Define, find and simplify the difference quotient of a given function; examples with detailed solutions are presented. A and B are points on the graph of f. A line passing trough the two points A ( x , f(x)) and B(x+h , f(x+h)) is called a secant line. The slope m of the secant line may be calculated as follows2.1 - Domain and Range Find the domain and range of f.... Ch. 2.1 - Torricellis Law A tank holds 50 gal of water, Consider the difference quotient formula. Find the components of the definition. Tap for more steps... . Since both terms are perfect squares, factor using the difference of squares formula, where.

Just replace a for x in f(x)=4x/(x-5) to get f(a)=4a/(a-5) just substitute h for x, to get f(h)=4h/(x-5) just exchange a+h for x to get f(a+h)=4(a+h)/(a+h-5) Take 3 above and subtract 1 above, to get f(a+h)-f(a) = 4(a+h)/(a+h-5) - 4a/(a-5) Try putting that expression everywhere a common denominator which is the fabricated from the two denominators

That gives numerator = 4(a+h)(a-5) -4a(a+h-5) in all places the new denominator: (a+h-5)(a-5)

Factor out the 4: 4[(a+h)(a-5)-a(a+h-5)] expand the factors within the brackets:

4[a^2+ha-5a-5h-a^2-ha+5a] = 4(-5h)=-20h Divide by way of h to get -20. That leaves

[f(a+h)-f(a)]/h = -20/(a+h+5)(a-5) That seems to be the resolution to 4, as given

But the entire level of this workout used to be actually to steer as much as discovering the limit of that expression as h is going to 0 as a limit.

so remaining step, exchange h=0 into the

denominator (a+h-5)(a-5) to get (a-5)^2

That leaves f'(a)=-20/(a-5)^2

That is the spinoff of the unique serve as f(a)=4x/(x-5) the spinoff is f'(a)=-20/(x-5)^2

You later learn a short cut technique to get that resolution, with out going via all this, to get the derivative of f(a) = -20/(x-5)^2 or for taking the spinoff of a fragment involving the variable.