show that the derivative of f(x) = ax^2 +bx+c is 2ax+b
To find the derivative of the function f(x) = ax^2 + bx + c, we can use the power rule for differentiation.
According to the power rule, if f(x) = ax^n, where a is a constant and n is a real number, then the derivative of f(x) is given by:
f'(x) = n(ax^(n-1))
Applying the power rule to each term of the function f(x), we have:
f'(x) = 2ax^1 + 1bx^0 + 0
Simplifying, we get:
f'(x) = 2ax + b + 0
Thus, the derivative of f(x) = ax^2 + bx + c is 2ax + b.