Consider the following function. f(x) = x2 + 3.5x − 6 (a) Write the derivative formula. f '(x) =
Question
Consider the following function.
(a) Write the derivative formula.
Solution
To find the derivative of the function f(x) = x^2 + 3.5x - 6, we need to apply the power rule, which states that the derivative of x^n is n*x^(n-1).
The derivative of x^2 is 2x (using the power rule with n=2).
The derivative of 3.5x is 3.5 (using the power rule with n=1).
The derivative of a constant, like -6, is 0.
So, the derivative of the function f(x) = x^2 + 3.5x - 6 is:
f'(x) = 2x + 3.5.
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