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Chapter 3: Q. 13 (page 260)

Find the critical points of the function
$f^{'} (x) = \sqrt{1 + x^{2}} - 4$

Short Answer

Expert verified

$Therefore the critical points are x = \pm \sqrt{(15)}$

Step by step solution

Step 1. Given

The given function is $f^{'} (x) = \sqrt{1 + x^{2}} - 4$ .

Step 2. Calculation

$S e t f' (x) = 0 t o d e t e r m i n e t h e c r i t i c a l p o i n t . \sqrt{1 + x ²} - 4 = 0 \sqrt{(1 + x^{2})} = 4 1 + x^{2} = 16 x^{2} = 16 - 1 x^{2} = 15 x = \pm \sqrt{(15)} Therefore the critical points are x = \pm \sqrt{(15)}$

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Most popular questions from this chapter

For each set of sign charts in Exercises 53–62, sketch a possible graph of f.

For each graph of f in Exercises 49–52, explain why f satisfies the hypotheses of the Mean Value Theorem on the given interval [a, b] and approximate any values c ∈ (a, b) that satisfy the conclusion of the Mean Value Theorem.

For each set of sign charts in Exercises 53–62, sketch a possible graph of f.

Use a sign chart for $f^{'}$ to determine the intervals on which each function $f$ is increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

role="math" localid="1648368106886" $f (x) = s i n (\frac{π}{2} x)$

Use a sign chart for $f^{'}$ to determine the intervals on which each function $f$ is increasing or decreasing. Then verify your algebraic answers with graphs from a calculator or graphing utility.

$f (x) = 2 x^{3} - 9 x^{2} + 1$

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Find the critical points of the functionf'(x)=1+x2-4

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

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Most popular questions from this chapter

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Find the critical points of the function
$f^{'} (x) = \sqrt{1 + x^{2}} - 4$