By first principle, Find the derivative of the function
iii.) f(x) = 3x^2 + 2x + 1
with respect to x at x = x subscript 0
To find the derivative of the function f(x) = 3x^2 + 2x + 1 at x = x0, we can use the power rule for differentiation.
The power rule states that the derivative of x^n with respect to x is n*x^(n-1).
Therefore, the derivative of f(x) = 3x^2 + 2x + 1 is:
f'(x) = d/dx [3x^2] + d/dx [2x] + d/dx [1]
f'(x) = 6x + 2
Now, to find the derivative at x = x0, we substitute x0 into the derivative function:
f'(x0) = 6*x0 + 2
f'(x0) = 6x0 + 2
Therefore, the derivative of the function f(x) = 3x^2 + 2x + 1 with respect to x at x = x0 is 6x0 + 2.