True or false, 15 seconds each: (a) If … then

39 True or false, 15 seconds each: (a) If $f(x)⩽g(x)$ then $df/dx⩽dg/dx$. (b) If $df/dx⩽dg/dx$ then $f(x)⩽g(x)$. (c) $xv(x)$ is odd if $v(x)$ is even. (d) If $v_{\text{ave}}⩽w_{\text{ave}}$ on all intervals then $v(x)⩽w(x)$ at all points.

True or false, 15 seconds each:
(a) If $f(x)\le g(x)$ then $df/dx\le dg/dx$.
(b) If $df/dx\le dg/dx$ then $f(x)\le g(x)$.
(c) $xv(x)$ is odd if $v(x)$ is even.
(d) If $v_{\text{ave}}\le w_{\text{ave}}$ on all intervals then $v(x)\le w(x)$ at all points.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §5.6 Properties of the Integral and Average Value, #39