For #$15-25,$ differentiate: $=$ denikatices

$15.f(x)=3x^2-7x+9$

$16.y=\sqrt[3]{x^2}+\frac{5}{x^3}$

$17.f(x)=\frac{x^4+2}{x^2}$

$18.y=(x^2-3x+3{)}^5$

$19.f(x)=(lnx)(5x^2+4{)}^3$

$20.y=ln(3x^2+2)$

$21.y=e^{2x-1}$

$22.f(x)=\frac{4x-e^x}{e^x}$

$23.y=-2x^2(3x^4+11{)}^5$

$24.f(x)=\frac{6x^2-2x}{e^{6x}}$

$25.f(x)=\frac{x^2+8}{8-x}$

$26.$ Find the equation of the tangent line to $y=x^3$ at the point $(-2,-8).$

$27.$ Find the equation of the tangent line to the graph of $y=x^2-\sqrt[\phantom{2}]{x}$ at the point $(4,14).$

$28.$ Find the point$($s$)$ on the graph of $y=-\frac{1}{3}{x}^3+6x^2-11x-50$ at which the tangent line is horizontal.

$29.$ Find the points on the graph of $f(x)=-0\mathrm{.}01x^2+2x$ at which the tangent line has slope $1.$

For #$30-34,$ find the absolute maximum and$/$or minimum values of the function on the interval shown.

$30.f(x)=\frac{2}{3}{x}^3-x^2-4x+5$;

$0,3$

$31.g(x)=2x-5$;$,(-,)$

$32.h(x)=-x^2+6x-4$;$,(-,)$

$33.f(x)=x+\frac{100}{x}$;$(0,)$

$34.f(x)=2x^3+4x^2+2x-5$;$,[-2,1]$

For #$35-42,$ integrate each of the following:

$35.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(3x^2-\frac{1}{x})dx$

$36.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(3\sqrt[3]{x^5}+5e^{-7x}+8)dx$

$37.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(\frac{3x^2}{x^3-3})dx$

$38.{\displaystyle \underset{0}{\overset{4}{}}}x{e}^{2x}dx$

$39.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}10x^4(x^5+18{)}^{7}dx$

$40.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x^5}{(x^6-8{)}^2}dx$

$41.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{2}lnxdx$

$42.{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x{e}^{-x^2}dx$