• 1.

  draft
  Finding the stationary points of a rational function with specific features.
• 2.

  draft
  Finding the stationary points of a cubic with two turning points
• 3.

  draft
  Maximising the volume of a rectangular box
• 4.

  draft
  Another practical application of differentiation
• 5.

  draft
  This question guides students through the process of determining the dimensions of a box to minimise its surface area whilst meeting a specified volume.
• 6.

  draft
• 7.

  draft
  Problem on a closed cylindrical tank having minimum surface area
• 8.

  draft
  Rate of change problem involving velocity & acceleration
• 9.

  Ready to use
  Implicit differentiation. Given $x^2+y^2+ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$.  
• 10.

  Ready to use
  Implicit differentiation. Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$. Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.  
• 11.

  draft
  Using basic derivatives to calculate the gradient function of a hill $y=-e^{x}+b\ln{\left(x\right)+c$, and then substituting values to find the gradient at specific distance from the sea. 
• 12.

  draft
  Calculating the rate of change of the temperature during a chemical reaction using the chain rule in a function of the form $T=ate^{-t}$, and finding the maximum temperature of the reaction.
• 13.

  draft

  Variable	Value	Description
  ans_c

• 14.

  draft

  Variable	Value	Description
  ans_c

• 15.

  Ready to use
  $I$ compact interval, $g:I\rightarrow I$, $g(x)=(x-a)(x-b)^2$. Stationary points in interval. Find local and global maxima and minima of $g$ on $I$. 
• 16.

  draft
  Optimisation using calculus rebel rebelmaths Rebel
• 17.

  Ready to use
  Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.
• 18.

  Ready to use
  Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.
• 19.

  Ready to use
  Just what the title says, I guess.
• 20.

  Ready to use
  Just what the title says, I guess.
• 21.

  Ready to use
  Just what the title says, I guess.
• 22.

  draft
  Displacement-time graphs are given and the student should select the correct velocity-time graphs from a list. Includes linear, piecewise linear and quadratic displacement-time functions.
• 23.

  draft
  Rotate the graph of  $y=a\ln(bx)$  by $2\pi$ radians about the $y$-axis between $y=c$ and $y=d$. Find the volume of revolution.
• 24.

  draft
  Rotate $y=a(\cos(x)+b)$ by $2\pi$ radians about the $x$-axis between $x=c\pi$ and $x=(c+2)\pi$. Find the volume of revolution.
• 25.

  draft
  Problem on a closed cylindrical tank having minimum surface area
• 26.

  draft
  Maximising the volume of a rectangular box
• 27.

  draft
• 28.

  draft
  Implicit differentiation. Given $x^2+y^2+dxy +ax+by=c$ find $\displaystyle \frac{dy}{dx}$ in terms of $x$ and $y$. Also find two points on the curve where $x=0$ and find the equation of the tangent at those points.  
• 29.

  draft
  Implicit differentiation question with customised feedback to catch some common errors.

There are no questions in this group.