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Can someone help me with some of these true and false questions. I will leave a like!!

True/False Questions Read each statement below carefully. Place a $T$ on the line if you think the statement it TRUE. Place an $F$ on the line if you think the statement is FALSE. (a) (1 point) If $f_{′}(c)=0$ and $f_{′′}(c)=0$, then by the second derivatve test the function does not have a local minimum or local maximum at $x=c$. (b) (1 point) If $f_{′}(c)=0$ and $f_{′′}(c)<0$, then the function has a local minimum at $x=c$ (c) (1 point) $F$ The function $f(x)=x1 $ has a absolute maximum on $[1,2]$. (d) (1 point) If $f_{′}(x)=0$ for all $x$, then $f$ is a constant function. (e) (1 point) If $f$ is continuous on $[1,3]$, differentiable on $(1,3)$, and satisfies $f(1)=2$ and $f(3)=$ 5 , then there exists a number $c$ satisfying $1<c<3$, such that $f_{′}(c)=3/2$. (f) (1 point) $lim_{x→−∞}x_{2}+1 3x =−3$ (g) (1 point) $→$ The function $f(x)=xe_{x} $ is increasing on $(1,∞)$ (h) ( 1 point) The function $f(x)=x_{3}(1−x)_{6}$ has no absolute extreme values.

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