how to differentiate (x^3) - 2 using [f(x+h)-f(x)]/h
just plug and chug
f(x+h)-f(x) = (x+h)^3 - 2 - (x^3-2) = 3hx^2 + 3h^2 x + h^3
Now divide by h and you have
3x^2 + 3hx + h^2
take the limit and you wind up with
3x^2
alright thanks
To differentiate the function (x^3) - 2 using the formula [f(x+h) - f(x)] / h, we can follow these steps:
Step 1: Start with the given function f(x) = (x^3) - 2.
Step 2: Substitute f(x) into the formula [f(x+h) - f(x)] / h.
[f(x + h) - f(x)] / h = [(x + h)^3 - 2 - (x^3 - 2)] / h
Step 3: Expand and simplify the numerator.
[(x + h)^3 - 2 - (x^3 - 2)] = [x^3 + 3x^2h + 3xh^2 + h^3 - 2 - x^3 + 2]
Simplifying further, we get:
= 3x^2h + 3xh^2 + h^3
Step 4: Substitute the simplified expression back into the formula.
[f(x + h) - f(x)] / h = (3x^2h + 3xh^2 + h^3) / h
Step 5: Simplify the expression.
= 3x^2 + 3xh + h^2
Step 6: To find the derivative, take the limit as h approaches 0.
lim(h -> 0) (3x^2 + 3xh + h^2) = 3x^2 + 0 + 0
The derivative of the function (x^3) - 2 using the formula [f(x+h) - f(x)] / h is 3x^2.