if a, b, c are the roots of the function 5x^3 - 11x^2 + 7x + 3, find a^2 + b^2 + c^2. (Find the derivative of the function)
Use the formula \(\frac{f(x+h)-f(x)}{h}\) to find the derivative.
\(\frac{f(x+h)-f(x)}{h}= \frac{[5(x+h)^3-11(x+h)^2+7(x+h)+3]-[5x^3-11x^2+7x+3]}{h}\)
\(=\frac{5x^3+15x^2h+15xh^2+5h^3-11x^2-22xh-11h^2+7x+7h+3-5x^3+11x^2-7x-3}{h}\)
\(=\frac{15x^2h+15xh^2+5h^3-22xh-11h^2+7h}{h}\)
\(= 15x^2+15xh + 5h^2 -22x-11h+7\)
Substitute the \(h\) with 0, \(= \boxed{15x^2-22x+7}\)
