Q. 84 Use the given derivative f'聽to ... [FREE SOLUTION]

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Chapter 3: Q. 84 (page 276)

Use the given derivative $f'$ to find any local extrema and inflection points of $f$ and sketch a possible graph without first finding an formula for $f$ .
$f' (x) = x^{4} - 1$

Short Answer

Expert verified

$x = 1$ is a local minimum point and $x = - 1$ is a local maximum point.

Step by step solution

Step 1. Given information

The function is given by $f' (x) = x^{4} - 1$ .

Step 2. Calculation

To find the critical points consider $f' (x) = 0$

$x^{4} - 1 = 0 (x - 1) (x + 1) (x^{2} + 1) = 0 鈬� x = 1, - 1$

So, the critical number is $x = 1, - 1$

Then consider the following table,

Interval	$(- 鈭�, - 1)$	$(- 1, 1)$	$(1, 鈭�)$
$k$	$- 2$	$0$	$2$
Test value for $f' (k)$	$+$	$-$	$+$
Sign of $f' (x)$	$f' (x) > 0$	$f' (x) < 0$	$f' (x) > 0$
Conclusion	Increasing	Decreasing	Increasing

So, $x = 1$ is a local minimum point and $x = - 1$ is a local maximum point.

Then the graph of $f,$

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91影视

Use the given derivative $f'$ to find any local extrema and inflection points of $f$ and sketch a possible graph without first finding an formula for $f$ .
$f' (x) = x^{4} - 1$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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91影视

Use the given derivative f'to find any local extrema and inflection points of fand sketch a possible graph without first finding an formula for f.f'(x)=x4-1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Geometry

Calculus

Logic and Functions

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

Use the given derivative $f'$ to find any local extrema and inflection points of $f$ and sketch a possible graph without first finding an formula for $f$ .
$f' (x) = x^{4} - 1$