WebRemember that the limit definition of the derivative goes like this: f '(x) = lim h→0 f (x + h) − f (x) h. So, for the posted function, we have. f '(x) = lim h→0 m(x + h) + b − [mx +b] h. By multiplying out the numerator, = lim h→0 mx + mh + b − mx −b h. By cancelling out mx 's and b 's, = lim h→0 mh h. By cancellng out h 's,

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

WebJun 9, 2014 · Best Answer f (a) = a 2 + 8 f (a+h) = (a+h) 2 + 8 = a 2 + 2ah + h 2 + 8 So: f (a+h) - f (a) = a 2 + 2ah + h 2 + 8 - ( a 2 + 8) = 2ah + h 2 and: (f (a+h) - f (a))/h = 2a + h … WebSep 13, 2024 · Explanation: To find f (a) and f (a + h) replace x in f (x) = 5 x +7 with a and a + h respectively. f (a +h) − f (a) = 5 a +h + 7 − 5 a +7. XXX = 5(a + 7) − 5(a +h + 7) (a + h … christmas gifts for college friends

Calculus Examples Functions Difference Quotient - Mathway

WebYou need \frac{f(a+h)-f(a)}{h}, but you seem to have computed something else not involving f. Try this, \begin{equation} \frac{f(a+h)-f(a)}{h}=\frac{(2-6(a+h)+4(a+h)^2)-(2 … Web1 day ago · By PATRICK WHITTLE April 12, 2024. PORTLAND, Maine (AP) — Somewhere in a remote stretch of forest near Maine’s border with Canada, rocks from space crashed to Earth and may be scattered across the ground — just waiting to be picked up. If you’re the first person to find a big one, a museum says it’ll pay out a $25,000 reward. WebStep 1: Identify the function f(x) f ( x) for which we are taking its first derivative at the point x = a, f′(a) x = a,... Step 2: Choose either the difference quotient or instantaneous rate of … gesh investments