o find the local extrema of the polynomial, we first take the derivative of the polynomial and set it equal to zero:
f(x) = 10x^5 + 22x^4 + 20x^3 - 0x^2 + 6
f'(x) = 50x^4 + 88x^3 + 60x^2
Setting f'(x) = 0, we can factor out a 2x^2 from the expression to get:
f'(x) = 2x^2(25x^2 + 44x + 30) = 0
Using the quadratic formula to solve for x, we get:
x = (-44 ± sqrt(44^2 - 4(25)(30))) / (2(25))
x = (-44 ± sqrt(784)) / 50
x = (-44 ± 28) / 50
x = -0.32 or -0.56