f(x) = 6x² - 4 estimate the instantaneous rate of change for x = 8?
For the function f(x) = 6x² - 4 estimate the instantaneous rate of
change for the given values of x.
a) x = -2
b) x = 8
I want to use the difference of quotient formula but i dont know how to plug in the equation and get the answer, can somebody please how me? i dont want the answer i have the ans, its -24 and 96.
formula =
f(x+h)−f(x)
----------------
.....h
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(a) You want the rate of change at x = -2.
h is a small number, for instance 0.01. x + h = -2 + 0.01 = -1.99.
Then applying the formula, you'd calculate [f(-1.99) - f(-2)] / 0.01
-24 is the exact rate of change. You're approximating it so you're going to get a number close to that but probably not equal to that. The smaller the value of h you choose, the closer your estimate will be.
only take the by-fabricated from the function and fill in x = 2. i will supply an occasion that resembles what you wrote, (yet i replaced into puzzled with the 2x4, so which you migth ought to take a closer look at it): D(x^3-x^2-2x)= 3x^2-2x-2 fill in x=2 and you get: 3*4-4-2=6 so f'(2)=6
Lim x->8 [f(8)-f(x)]/(8-x)
=[384-4-6x^2+4]/(8-x)
=(384-6x^2)/(8-x)
=6(64-x^2)/(8-x)
=6(8+x)(8-x)/(8-x)
=6(x+8)
Plug in 8 for x and get 6*16=96
Lim x->-2 [f(-2)-f(x)]/(-2-x)
=[24-4-6x^2+4]/(-1)(2+x)
=(6x^2-24)/(x+2)
=6(x^2-4)/(x+2)
=6(x+2)(x-2)/(x+2)
=6(x-2)
Plug in -2 and get 6(-2-2)=-24