The function $f(x)=x^3-2x^2$ is increasing over which of the following intervals?

$($a$)x<mn>0</mn>$ only

$($b$)x>\frac{4}{3}$ only

$($c

$(d)x<mn>0</mn>$ and $x>\frac{4}{3}$

Read this very carefully. Given the graph $ofg(below),$ which $of$ the following correctly defines $g^{\text{'}}?$

$(a)g^{\text{'}}(x)=sinx$

$(b)g^{\text{'}}(x)=-sinx+3$

$(c)g^{\text{'}}(x)=-cosx+3$

$(d)g^{\text{'}}(x)=-sinx$

Find $y^{\text{'}}if$

$y=co{s}^{2}x-si{n}^{2}x$

$(a)0$

$(b)-1$

$(c)-2(cosx+sinx)$

$(d)-2sin(2x)$

$4.$ The equation $of$ the line tangent $to$ the graph $of$

$y=\frac{2x+3}{3x-2}$

$at$ the point $(1,5)is$:

$(a)x-13y=64$

$(b)-2x+3y=13$

$(c)13x-y=8$

$(d)13x+y=18$

$5.$ Find $\frac{dy}{dx}atx=2if$

$x^2+xy=10$

$(a)\frac{2}{7}$

$(b)\frac{3}{2}$

$(c)-\frac{7}{2}$

$(d)-2$ Please :)