To find the derivative of the function f(x) = 10x² + 4x, we will apply the power rule of differentiation.
The power rule states that if f(x) = ax^n, then f'(x) = n imes ax^{n-1}.
Let’s differentiate each term of f(x):
- The derivative of 10x² is 2 imes 10x^{2-1} = 20x.
- The derivative of 4x is 4 (since the derivative of x is 1).
Putting it all together, we get:
f'(x) = 20x + 4
Now, we need to evaluate this derivative at x = 11:
f'(11) = 20(11) + 4
Calculating this gives us:
f'(11) = 220 + 4 = 224
So, the derivative of f(x) at x = 11 is 224.