Chapter 3: Q. 6 (page 247)

Suppose that $f$ is defined for $x = 0$ and differentiable everywhere except at $x = 0$ and $x = 1$ , and that $f' (x) = 0$ only at $x$ = ±2. List all the critical points of f and sketch a possible graph of $f$ .

Short Answer

Expert verified

$f (x) = 0.2 x^{5} - 0.25 x^{4} - 1.33 x^{3} - 2 x^{2}$

Step by step solution

Step1. Given Information

$The function is defined for x \neq 0 and is differentiable at all points except at x = 0 and x = 1 and that f^{'} (x) = 0 only at x = \pm 2$

Step 2. Calculations

$The critical points of the function, therefore will be x = - 2; x = 0; x = 1; x = 2 Therefore, the differentiation of the function will be f^{'} (x) = x (x + 2) (x - 2) (x - 1) The graph can be drawn as$

$Therefore, the function is f (x) = 0.2 x^{5} - 0.25 x^{4} - 1.33 x^{3} - 2 x^{2}$

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Suppose that $f$ is defined for $x = 0$ and differentiable everywhere except at $x = 0$ and $x = 1$ , and that $f' (x) = 0$ only at $x$ = ±2. List all the critical points of f and sketch a possible graph of $f$ .

Short Answer

Step by step solution

Step1. Given Information

Step 2. Calculations

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Suppose that fis defined for x=0and differentiable everywhere except at x=0and x=1, and that f'(x)=0only at x= ±2. List all the critical points of f and sketch a possible graph of f.

Short Answer

Step by step solution

Step1. Given Information

Step 2. Calculations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

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Study anywhere. Anytime. Across all devices.

Suppose that $f$ is defined for $x = 0$ and differentiable everywhere except at $x = 0$ and $x = 1$ , and that $f' (x) = 0$ only at $x$ = ±2. List all the critical points of f and sketch a possible graph of $f$ .