Chapter 2: Q 23. (page 222)
Find the derivatives of the functions:
The required answer is.
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The following reciprocal rules tells us hoe to differentiate the reciprocal of a function
Prove this using
a) definition of the derivative
b) by using the quotient rule
Suppose f is a polynomial of degree n and let k be some integer with . Prove that if f(x) is of the form
Then where is the k-th derivative of
A tomato plant given ounces of fertilizer will successfully bear pounds of tomatoes in a growing season.
(a) In real-world terms, what does represent and what are its units? What does represent and what are its units?
(b) A study has shown that this fertilizer encourages tomato production when less than ounces are used, but inhibits production when more than ounces are used. When is positive and when is negative? When is positive and when is negative?
Differentiation review: Without using the chain rule find the derivative of each of the function f that follows some algebra may be required before differentiating
If Katie walked at miles per hour for minutes and then sprinted at miles an hour for minutes, how fast would Dave have to walk or run to go the same distance as Katie did at the same time while moving at a constant speed? Sketch a graph of Katie’s position over time and a graph of Dave’s position over time on the same set of axes.
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