Chapter 2: Q 2. (page 237)
Translate expressions written in Leibniz notation to “prime” notation, and vice versa.
Chapter 2: Q 2. (page 237)
Translate expressions written in Leibniz notation to “prime” notation, and vice versa.
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Get started for freeProve that if f is a quadratic polynomial function then the coefficient of f are completely determined by the values of f(x) and its derivatives at x=0 as follows
Find the derivatives of the functions in Exercises 21–46. Keep in mind that it may be convenient to do some preliminary algebra before differentiating.
Velocity is the derivative of position . It is also true that acceleration (the rate of change of velocity) is the derivative of velocity. If a race car’s position in miles t hours after the start of a race is given by the function , what are the units of ? What are the units and real-world interpretation of ? What are the units and real-world interpretations of ?
Use the definition of the derivative to find for each function f in Exercises 39-54
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
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