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# derivatives

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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)

Jul 17, 2022

#1
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a^2 + b^2 + c^2 = -734/5

Jul 17, 2022
#2
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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, $$= \boxed{15x^2-22x+7}$$

Jul 18, 2022