Chapter 2: Q. 4 (page 209)
In the text we noted that if was a composition of three functions, then its derivative is . Write this rule in “prime” notation.
Short Answer
In prime notation the derivative is:
Chapter 2: Q. 4 (page 209)
In the text we noted that if was a composition of three functions, then its derivative is . Write this rule in “prime” notation.
In prime notation the derivative is:
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Get started for freeWrite down a rule for differentiating a composition of four functions
(a) in “prime” notation and
(b) in Leibniz notation.
For each function and interval in Exercises , use the Intermediate Value Theorem to argue that the function must have at least one real root on . Then apply Newton’s method to approximate that root.
localid="1648369345806" .
Suppose h(t) represents the average height, in feet, of a person who is t years old.
(a) In real-world terms, what does h(12) represent and what are its units? What does h' (12) represent, and what are its units?
(b) Is h(12) positive or negative, and why? Is h'(12) positive or negative, and why?
(c) At approximately what value of t would h(t) have a maximum, and why? At approximately what value of t would h' (t) have a maximum, and why?
For each function graphed in Exercises 65-68, determine the values of at which fails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.
For each function graphed in Exercises 65-68, determine the values of at which fails to be continuous and/or differentiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.
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