Which is the following statement true?

a$)f(x)$ is concave up in the interval $(-,a)$

$($b$)f(x)$ is concave down in the interval $(a,c)$

c$)f(x)$ has two points of inflection.

d$)f(x)$ has relative minimum at $x=b$

e$)f(x)$ is concave down in the interval $(b,c)$

Which is the following statement false?

a$)f^{\text{'}}(x)$ is decreasing in the interval $(-,a)$

b$)f^{\text{'}}(x)$ is increasing in the interval $(c,)$

c$)f^{\text{'}}(x)$ has three points of inflection.

d$)f^{\text{'}}(x)$ has relative minimum at $x=a$

e$)f^{\text{'}}(x)$ has relative maximum at $x=b$

Let $s=t^2-6t-12$; find the maximum speed of the particle during the time interval $0t7$

a$)5$

b$)6$

c$)7$

$($d$)8$

e$)9$

Let $s=2t^3-12t^{2}4t9$; find $s$ and $v$ when $a=0.$

a$)-15$ and $-14$

b$)-14$ and $20$

c$)-15$ and $-20$

d$)15$ and $-20$

e$)$ None of these

The position function of a particle is given by $s=4t^3-12t^{2}9t-1$ for $t0.$ which are the following statements false $?$

a$)t=\frac{3}{2}t=\frac{5}{2}0,$ the particle $is$ moving right direction$\mathrm{.}0,$ the particle $is$ moving left direction.

$(e)t=\frac{5}{2},$ the particle stops.

$f0,$ the particle $is$ slowing down.

$c\frac{1}{2},$ the particle $is$ speeding $up.$

$b$