For what interval of x-values is the curve y = f (x) concave up?

The first derivative of the function f is defined by f'(x) = (x2 +1)sin(3x - 1) for -1.5 < x < 1.5. On which of the following intervals is the graph of f concave up?Responses(−1.5, −1.341) and (−0.240, 0.964)(−1.5, −1.341) and (−0.240, 0.964)(−1.341, −0.240) and (0.964, 1.5)(−1.341, −0.240) and (0.964, 1.5)(−0.714, 0.333) and (1.381, 1.5)(−0.714, 0.333) and (1.381, 1.5)(−1.5, −0.714) and (0.333, 1.381)

determine\:the\:intervals\:of\:concavity\:and\:the\:points\:of\:inflection\:for\:the\:curve\:y=3x^5-40x^3+3x-20

The table gives values for a polynomial function 𝑔 at selected values of 𝑥. If 𝑎<𝑏, then 𝑔𝑎>𝑔𝑏 for all 𝑎 and 𝑏 in the interval 3<𝑥<7. Which of the following could be true about the graph of 𝑔 on the interval 3<𝑥<7 ?ResponsesThe graph of 𝑔 is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of  g  is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of 𝑔 is concave up because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of  g  is concave up because the function is decreasing, and the average rate of change over equal-length input-value intervals is increasing.The graph of 𝑔 is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.The graph of  g  is concave down because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.The graph of 𝑔 is concave up because the function is decreasing, and the average rate of change over equal-length input-value intervals is decreasing.

determine\:the\:interval\:of\:concavity\:and\:the\:point\:of\:inflection\:of\:the\:curve\:y=e^{-x^2}\:.Also\:,\:show\:that\:the\:points\:of\:inflection\:of\:the\:\:curve\:y=-\left(x-3\right)\:\sqrt{X-5}\:lies\:on\:the\:line\:3x=17

What is Concave up and Concave down of f(x)=(5x^2)/(5x^2+3)