CPM Homework Help : CALC Problem 4-19

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Home > CALC > Chapter Ch4 > Lesson 4.1.2 > Problem 4-19

4-19.

For each $f(x)$ , find its general antiderivative, $F(x)$ .

Hint:

Just as $f^\prime(x)$ is the slope function of $f(x)$ , $f(x)$ is the slope function of $F(x)$ .

$f(x) =-2$
Hint (a):
If the slope function, $f(x)$ , is horizontal, then the original function, $F(x)$ , is _______________.
Answer (a):
If $f(x)$ is horizontal, then $F(x)$ will be linear: $F(x) = -2x + C$

$f ( x ) = \frac { 3 } { 2 } x ^ { - 1 / 2 }$
Hint (b):
Check your work by finding the derivative of $F(x)$ . Are your $+$ and $−$ signs correct?

f(x) = −3x² + 6x
Hint (c):
For all of these, don't forget the $+C$ .

f(x) = 2(x + 3)
Hint (d):
If the slope function, $f(x)$ , is linear, then the original function, $F(x)$ , will be _____________________________.

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