𝑓(𝑥) = 2𝑥^2 − 𝑥 + 6 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑣𝑎𝑙𝑢𝑒𝑠 𝑜𝑓 𝑥

Question

^{Determine whether each of the following functions is (a) continuous (b) differentiable with solution}

Answer 1

f(x) = y = 2x^2 -x + 6

x = 1/4 + or - (1/4)sqr(1-48)

x= 1/4 + or - (1/4)sqr-47

x= 1/4 + or -(i/4)sqr47

two imaginary solutions, no real solution

the polynomial is an upward opening parabola which never intersects the x axis It has no x intercepts. Its y intercept is (0,6)

it's continuous and differentiable

it's everywhere above the x axis It has an axis of symmetry at x= 1/4

its vertex is (1/4, 5 7/8) = minimum point