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Chapter 2: Q 20. (page 222)

Find the derivatives of each of the functions in excercises

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a

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Most popular questions from this chapter

Use the definition of the derivative to prove the following special case of the product rule

$\frac{d}{d x} (x^{2} f (x)) = 2 x f (x) + x^{2} f' (x)$

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The line that passes through the point $(3, 2)$ and is parallel to the tangent line to $f (x) = \frac{1}{x}$ at $x = - 1$ .

Prove that if f is a quadratic polynomial function $f (x) = a x^{2} + b x + c$ then the coefficient of f are completely determined by the values of f(x) and its derivatives at x=0 as follows

$a = \frac{f " (0)}{2}; b = f' (0); c = f (0)$

Velocity $v (t)$ is the derivative of position $s (t)$ . It is also true that acceleration $a (t)$ (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 $s (t)$ , what are the units of $s (1.2)$ ? What are the units and real-world interpretation of $v (1.2)$ ? What are the units and real-world interpretations of $a (1.2)$ ?

Use (a) the $h \to 0$ definition of the derivative and then

(b) the $z \to c$ definition of the derivative to find $f' (c)$ for each function f and value $x = c$ in Exercises 23–38.

27. $f (x) = 1 - x^{3}, x = - 1$

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Find the derivatives of each of the functions in excercises

Short Answer

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a

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