(Solved): Can someone help me with some of these true and false questions. I will leave a like!! True/Fal ...

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 $\mathbf{T}$ 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 $f^{\prime }(c)=0$ and $f^{\prime \prime }(c)=0$, then by the second derivatve test the function does not have a local minimum or local maximum at $x=c$. (b) (1 point) If $f^{\prime }(c)=0$ and $f^{\prime \prime }(c)<0$, then the function has a local minimum at $x=c$ (c) (1 point) $\stackrel{F}{}$ The function $f(x)=\frac{1}{x}$ has a absolute maximum on $[1,2]$. (d) (1 point) If $f^{\prime }(x)=0$ 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 $f^{\prime }(c)=3/2$. (f) (1 point) ${\lim }_{x\to -\infty }\frac{3x}{\sqrt{x^2+1}}=-3$ (g) (1 point) $\to$ The function $f(x)=\frac{e^x}{x}$ is increasing on $(1,\infty )$ (h) ( 1 point) The function $f(x)=x^3(1-x{)}^6$ has no absolute extreme values.