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b) Determine by differentiation the value of r for which V has a stationary value. c) Show that the value of r found in part (b) gives the maximum value for V. d) Calculate, to the nearest cm 3, the maximum volume of the pencil holder. 120 r 6.18 π = ≈ , Vmax ≈ 742 r h

Drill problems on derivatives and antiderivatives 1 Derivatives Find the derivative of each of the following functions (wherever it is de ned): 1. f(t) = t2 + t3 1 t4 Answer: f0(t) = 2 t3 1 t2 + 4 t5 2. y= 1 3 p x + 1 4 Answer: dy dx = 1 6x p x 3. f(t) = 2t3 004t2 + 3t 1. Also nd f (t):

Related rate problems involve equations where there is some relationship between two or more derivatives. We solved examples of such equations when we studied ...

The purpose of this Collection of Problems is to be an additional learning resource for students who are taking a di erential calculus course at Simon Fraser University. The Collection contains problems given at Math 151 - Calculus I and Math 150 - Calculus I With Review nal exams in the period 2000-2009. The problems are

Here is a set of practice problems to accompany the Differentiation Formulas section of the Derivatives chapter of the notes for Paul ...

DIFFERENTIATION . Created by T. Madas Created by T. Madas Question 1 Evaluate the following. a) d (5x6) dx d ( )5 30x x6 5 dx = b) 3 2 2 d x dx ...

problems for you to practice what you have learned. At the end of the booklet you will find answers for each of the sections. Included are some pages for you to make notes that may serve as a reminder to you of any possible areas of difficulty. You should seek help with such areas of difficulty from your tutor or other university support services.

A sufficient condition to ensure the function is differentiable is that the partial derivatives all exist and are continuous. This concept was ...

Question 1 (non calculator). For each of the following curves find an equation of the tangent to the curve at the point whose x coordinate is given.

DIFFERENTIATION OF FUNCTIONS OF A SINGLE VARIABLE. 31. Chapter 6. DEFINITION OF THE DERIVATIVE ... Problems. 115. 15.4. Answers to Odd-Numbered Exercises.

problem using the function s(t) = 16t2, representing the distance down measured from the top. Then all the speeds are positive instead of negative.) b) Solve h(t) = 0 (or s(t) = 400) to find landing time t = 5. Hence the average speed for the last two seconds is h(5) − 2h(3) = 0 − (400 − 16 · 3 ) = −128ft/sec 2 2 3

The following questions involve derivatives. (a) Evaluate Dt cos−1(cosh(e−3t)), without simplifying your answer. (b) Use logarithmic differentiation to ...

30.04.2019 · Created by T. Madas Created by T. Madas Question 3 (***) The figure above shows a solid brick, in the shape of a cuboid, measuring 5x cm by x cm by h cm . The total surface area of the brick is 720 cm 2. a) Show that the volume of the brick, V cm 3, is given by 300 25 3 6 V x x= − . b) Find the value of x for which V is stationary. c) Calculate the maximum value for V, fully …

8 Basic Differentiation - A Refresher 4. Differentiation of a simple power multiplied by a constant To differentiate s = atn where a is a constant. Example • Bring the existing power down and use it to multiply. s = 3t4 • Reduce the old power by one and use this as the new power.

fortnightly, or monthly basis, you spend a few minutes practising the art of finding derivatives. You may find it a useful exercise to do this with friends and to discuss the more difficult examples. To build speed, try calculating the derivatives on the first sheet mentally … and have a friend or parent check your answers.

1C-6 Graph the derivative of the following functions directly below the graph of the function. It is very helpful to know that the derivative of an odd function ...

You can also do this whole problem using the function s(t) = 16t2, representing the distance down measured from the top. Then all the speeds are positive ...

278 CHAPTER 5. TECHNIQUES OF DIFFERENTIATION this general formula agrees with the specific value f′(2) = 12 we have already obtained. Notice the difference between the statements f′(x) ≈ ∆y/∆x and f′(x) = 3x2. For a particular value of ∆x, the corresponding value of ∆y/∆x is an approx-imation of f′(x). We can obtain ...

The rules of differentiation are straightforward, but knowing when to use them and in what order ... to differentiate the second, the chain rule is needed.

The problem of numerical differ- entiation is to compute an approximation to the derivative f of f by suitable combinations of the known values of f . A typical ...

The purpose of this Collection of Problems is to be an additional learning resource for students who are taking a di erential calculus course at Simon Fraser University. The Collection contains problems given at Math 151 - Calculus I and Math 150 - Calculus I With Review nal exams in the period 2000-2009. The problems are