determine-the-intervals-on-which-the-function-gx2x618x545x450-gx-2x6-18x5-45x4-5

Question

Determine the intervals on which the function g(x)=2x6−18x5+45x4+50 g(x) = $$2x^6$$ - $$18x^5$$ + $$45x^4 + 50  is $$concave up or concave down. Identify any inflection points.

Accepted Answer

Concave up on (−∞,∞)\left(-\infty,\infty\right)No inflection points

Answer

Concave up on (−∞,0)\left(-\infty,0\right)Concave down on (0,∞)\left(0,\infty\right)Inflection point at x=0x=0

Answer

Concave up on (−∞,3)\left(-\infty,3\right)Concave down on (3,∞)\left(3,\infty\right)Inflection point at x=3x=3

Answer

Concave up on (−∞,0)∪(3,∞)\left(-\infty,0\right)\cup\left(3,\infty\right)Concave down on (0,3)\left(0,3\right)Inflection points at x=0,3x=0,3

Determine the intervals on which the function g(x)=2x6−18x5+45x4+50 g(x) = 2x^6 - 18x^5 + 45x^4 + 50 is concave up or concave down. Identify any inflection points.

Determine the intervals on which the function $g (x) = 2 x^{6} - 18 x^{5} + 45 x^{4} + 50$ is concave up or concave down. Identify any inflection points.