At which value of $x$ does $u(x)=2x^3-15x^2+36x$ take its absolute MINIMUM on $\left[-5,4\right]$?

On which set is $v(x)=2x^3-12x^2+18x$ INCREASING?

At which value of $x$ does $f(x)=2x^3-18x^2+48x$ take its absolute MINIMUM on $\left[-6,5\right]$?

Find the value of $c$ the Mean Value Theorem guarantees for $q(x)=x^2+7x$ on $\left[-1,7\right]$.

On which set is $s(x)=2x^3+21x^2+72x$ DECREASING?

Find the absolute MAXIMUM VALUE of $g(x)=2x^3-3x^2-12x$ on $\left[-6,6\right]$.

Find the absolute MAXIMUM VALUE of $w(x)=2x^3-9x^2-24x$ on $\left[-3,6\right]$.

For $f(x)=2x^3+6x^2-48x$, use the Second Derivative Test to classify the critical point at $x=2$.

For $f(x)=2x^3+3x^2-12x$, use the Second Derivative Test to classify the critical point at $x=-2$.

A rectangle has perimeter $28$ centimeters, so a side of length $x$ gives area $A(x)=x\left(14-x\right)$ for $0\le x\le 14$. What is the greatest possible AREA, in square centimeters?

Classify every critical point of $f(x)=2x^3-3x^2-72x$.

For $v(x)=2x^3+3x^2-72x$, use the Second Derivative Test to classify the critical point at $x=-4$.

Classify every critical point of $v(x)=2x^3-6x^2-18x$.

A continuous function is negative at one end of an interval and positive at the other. Which theorem guarantees a root inside?

On which set is $p(x)=2x^3-54x$ CONCAVE DOWN?

A rectangle has perimeter $16$ centimeters, so a side of length $x$ gives area $A(x)=x\left(8-x\right)$ for $0\le x\le 8$. What is the greatest possible AREA, in square centimeters?

A differentiable function has $p^{\prime }\left(x\right)=-\left(x-4\right)\left(x-5\right)$. Where does $p$ have a relative MINIMUM?

The figure shows the graph of $u^{\prime }$, the DERIVATIVE of $u$. At which value of $x$ does $u$ have a relative MAXIMUM?

The figure shows the graph of $g^{\prime }$, the DERIVATIVE of $g$. On which set is $g$ INCREASING?

A differentiable function has $p^{\prime }\left(x\right)=-\left(x+2\right)\left(x-4\right)$. Where does $p$ have a relative MAXIMUM?

On which set is $s(x)=2x^3+9x^2$ DECREASING?

Find the value of $c$ the Mean Value Theorem guarantees for $v(x)=x^2-9x$ on $\left[2,6\right]$.

Find every critical point of $f(x)=2x^3+9x^2+12x$.

A rectangle has perimeter $36$ centimeters, so a side of length $x$ gives area $A(x)=x\left(18-x\right)$ for $0\le x\le 18$. What is the greatest possible AREA, in square centimeters?

On which set is $v(x)=2x^3+21x^2+72x$ INCREASING?

A rectangle has perimeter $12$ centimeters, so a side of length $x$ gives area $A(x)=x\left(6-x\right)$ for $0\le x\le 6$. What is the greatest possible AREA, in square centimeters?

Find the absolute MAXIMUM VALUE of $v(x)=2x^3+15x^2+36x$ on $\left[-6,1\right]$.

Find every critical point of $q(x)=2x^3-9x^2-24x$.

Find every critical point of $g(x)=2x^3+3x^2$.

On which set is $q(x)=2x^3-24x$ DECREASING?

At which value of $x$ does $u(x)=2x^3-6x$ take its absolute MINIMUM on $\left[-3,6\right]$?

Classify every critical point of $w(x)=2x^3+3x^2-36x$.

On which set is $v(x)=2x^3+9x^2+12x$ DECREASING?

A rectangle has perimeter $24$ centimeters, so a side of length $x$ gives area $A(x)=x\left(12-x\right)$ for $0\le x\le 12$. What is the greatest possible AREA, in square centimeters?

For $v(x)=2x^3-6x^2-18x$, use the Second Derivative Test to classify the critical point at $x=-1$.

On which set is $g(x)=2x^3-15x^2+24x$ DECREASING?

Find every critical point of $q(x)=2x^3-15x^2+24x$.

A rectangle has perimeter $32$ centimeters, so a side of length $x$ gives area $A(x)=x\left(16-x\right)$ for $0\le x\le 16$. What is the greatest possible AREA, in square centimeters?

The figure shows the graph of $g^{\prime }$, the DERIVATIVE of $g$. At which value of $x$ does $g$ have a relative MINIMUM?

For $q(x)=2x^3-24x$, use the Second Derivative Test to classify the critical point at $x=2$.