find tha value of f(x)=x3 where f(x+h)-f(x)/h
so far I got 3x2+3hx+h2/h and got stuck from here.
Perhaps you have
f(x) = x^3 (do you have a typo?)
and you want f'(x) ?
f(x+h) = (x+h)^3 = x^3 + 3 x^2h + 3 xh^2 + h^3
subtract x^3
f(x+h) -f(x) = 3 x^2h + 3 xh^2 + h^3
divide by h
3 x^2 + 3 xh + h^2
let h -->0 for derivative
f'(x) = 3 x^2 (the right answer)
0.3 (3x + 9)>or equal to 1.2 -(x+2)
To find the value of the expression (f(x+h) - f(x))/h for the function f(x) = x^3, you're on the right track. Let's continue simplifying the expression.
Step 1: Replace f(x) with x^3 and f(x+h) with (x+h)^3 in the expression.
(f(x+h) - f(x))/h = ((x+h)^3 - x^3)/h
Step 2: Expand the numerator using the binomial expansion formula (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.
((x+h)^3 - x^3)/h = ((x^3 + 3x^2h + 3xh^2 + h^3) - x^3)/h
Step 3: Simplify the expression by canceling out terms.
((x^3 + 3x^2h + 3xh^2 + h^3) - x^3)/h
Cancel out x^3 and -x^3:
(3x^2h + 3xh^2 + h^3)/h
Step 4: Factor out an h from the numerator:
(3x^2h + 3xh^2 + h^3)/h = h(3x^2 + 3xh + h^2)/h
Step 5: Cancel out h:
h(3x^2 + 3xh + h^2)/h = 3x^2 + 3xh + h^2
Therefore, the simplified expression is 3x^2 + 3xh + h^2.
So, the value of (f(x+h) - f(x))/h for the function f(x) = x^3 is 3x^2 + 3xh + h^2.