Evaluate the difference quotient, f(x)=4+3x-x^2, f(3+h)-f(3)/h thankyou please help me with this problem.?
f(3+h) = 4 + 3(3+h) - (3+h)^2 = 4 + 9 + 3h- 9 - 6h - h^2 = 4 - 3h - h^2 f(3) = 4 + 3(3) - (3)^2 = 4 + 9 - 9 = 4 f(3+h)-f(3) = 4-3h-h^2 - 4 = -3h-h^2 divide by h, -3-h Assuming you are doing the calculus derivatives, lim (h -> 0), so you get -3. So the slope of the tangent of the function 4+3x-x^2 at x = 3 is -3
Evaluating Difference Quotient Help?
Well given that this is assignment one, you may or may not have learned that the equation limit h -> 0 [ƒ(x+h)-ƒ(x)] / h, is exactly the definition of a derivative. Later on you will learn how to do derivatives without having to use this Definition. That being said, lets go back a little bit to function notation. Lets say that you are given the equation that f(x) = 4 + 3x - x², and a question asks you to find the value of the function when x is equal to 10. The question might state, find f(10)? The same notation applies to the difference quotient. The difference is that when you use this definition you plug (3+h) in every time you see an x in the original equation and then subtract f(3) then divide by h. In these types of problems Algebra is very important. If the problem just asks for the difference quotient and not the limit of the difference quotient this is not as important but you should practice good simplifying skills as it will come up a lot later in the course. --------------------------------------... So now a brief walk-through, First plug 3+h into the equation 4 + 3x - x², for every x in the equation. Second Plug 3 into the equation. Three, Collect like terms, simplify Four, divide by h Five, if needed evaluate the limit as h approaches zero, if it isn't needed then just stop after you have divided h thought the numerator. Best of Luck!
Evaluate difference quotient for f(x)=4+3x-x^2; f(3+h)-f(3)/h?
Essentially all you're doing is that with the f(3+h) and the f(3), you would take the value in parentheses and substitute that into the equation for x in f(x)=4+3x-x^2 and solve normally. So for example, f(3+h) means you would substitute (3+h) in for "x" in f(x), which produces: f(3+h) = 4 + 3(3+h) - (3+h)^2 = 4 + 9 + 3h - (9 + 6h + h^2) = 13 +3h -9 -6h -h^2 = 4 - 3h - h^2 And similarly, f(3) would simply be substituting the 3 in for "x" in f(x) to get: f(3) = 4 + 3(3) - (3)^2 = 4 I am assuming the last part of your equation is ALL divided by "h" as opposed to just f(3)/h which would be 4/h. In this case, your answer would be [(4-3h-h^2) - 4] / h = -3 - h If it was 4/h though, you would need to multiply f(3+h) by "h" to have "h" as an LCD like so: (4h-3h^2-h^3)/h - 4/h = (4h-3h^2-h^3-4)/h Hope that helped! (:
Let f(x)=x^3-13x. Calculate the difference quotient f(3+h)-f(3) / h For:?
Let f(x)=x^3-13x. Calculate the difference quotient f(3+h)-f(3) / h For: h=.1 =? h= -.1 =? h=.01 =? h= -.01 =? The slope of the tangent line to the graph of f(x) at x=3 is m=f '(3) =? PLEASE HELP. THANK YOU.
Evaluate the difference quotient for the given function. simplify answer. f(x)=4+3x-x^2, (f(3+h)-f(3))/h?
f(x) = 4 + 3x - x^2 f(3 + h) = 4 + 3(3 + h) - (3 + h)^2 f(3 + h) = 4 + 9 + 3h - 9 - 6h - h^2 f(3 + h) = 4 - 3h - h^2 f(3) = 4 + 3(3) - 3^2 f(3) = 4 + 9 - 9 f(3) = 4 f(3 + h) - f(3) = 4 - 3h - h^2 - 4 f(3 + h) - f(3) = - 3h - h^2 [f(3 + h) - f(3)] / h = (- 3h - h^2) / h [f(3 + h) - f(3)] / h = -3 - h
Couple of difference quotient problems?
For the first one: f(5+h) = 2 - 2(5+h) - (5+h)^2 = 2 - 10 - 2h - 25 - 10h - h^2 = -33 - 12h - h^2 f(5) = 2 - 2x5 - 5^2 = 2 - 10 - 25 = -33. So f(5+h)-f(5) = -12h - h^2. [f(5 + h) - f(5)]/h = (-12h - h^2)/h = -12 - h. For the second: f(3) = (3+5)/(3+3) = 8/6 = 4/3. So f(x) - f(3) = (x+5 )/(x+3) - 4/3 =(3x+15)/(3x+9)-(4x+12)/(3x+9) (after cross multiplying) =(-x+3)/(3x+9) [f(x) - f(3)]/(x-3) = [(-x+3)/(3x+9)]/(x-3) =(-x+3)/[(3x+9)(x-3)] (after multiplying top and bottom by 3x+9) = -1/(3x+9).
Evaluate the difference quotient for the given function. Simplify the answer.?
Proceed by etaps. Knowing that f (x) = 4 + 3x - x^2, Apply it to 3: f(3) = 4 + 9 - 9 = 4 Apply it to 3+h: f (3+h) = 4+9+3h - (3+h)^2 = 4+ 9 + 3h -9 -6h - h^2 = 4 -3h -h^2 Compute the difference: f (3+h) - f(3) = -3h - h^2 = h ( - 3 - h) Divide by h: [f (3+h) - f(3)] / h = - 3 - h Here is your result! Hope it helps!
If the remainder of a number is 3 and 2 when divided by 5 and 7 respectively, what will the remainder of the same number be when divided by 35, and how is this done?
Remainder of a number is 3 and 2 when divided by 5 and 7 respectively,Let the number be N. Thus the number N can be written in the following forms.N = 5x + 3 — (1)N = 7y + 2 — (2)where x and y are the whole numbers. So subtracting eqn(1) from eqn(2), we get0 = 7y -5x-1,i.e 7y = 5x + 1, so the minimum values of x and y satisfying this eqn by trail and error method would be x=4 and y=3,Substituting value of x in equation (1), we get N=23.Hence the minimum value of N=23And N can be anything of the form N=35k+23, where k is the whole number. Hence the remainder when N is divided by 35 is 23.
Find a simplified form of the difference quotient. Give your answer using the form Ax + Bh + C?
The difference quotient formula is (f(x + h) - f(x))/h. By difference quotient, we obtain: f(x + h) = 10(x + h)² + 8(x + h) - 1 => 10(x² + 2xh + h²) + 8x + 8h - 1 => 10x² + 20xh + 10h² + 8x + 8h - 1 f(x) = 10x² + 8x - 1 (10x² + 20xh + 10h² + 8x + 8h - 1 - (10x² + 8x - 1))/h => (10x² + 20xh + 10h² + 8x + 8h - 1 - 10x² - 8x + 1)/h => (10h² + 20hx + 8h)/h => h(10h + 20x + 8)/h => 10h + 20x + 8 Therefore: A = 20 B = 10 C = 8 I hope this helps!