Chapter 3: Q. 5 (page 247)

Suppose that $f$ is defined on (−∞,∞) and differentiable everywhere except at $x = - 2$ and $x = 4$ , and that $f' (x) = 0$ only at $x = 0$ and $x = 5$ . List all the critical points of $f$ and sketch a possible graph of $f$ .

Short Answer

Expert verified

$f (x) = 0.2 x^{5} - 1.75 x^{4} + 0.67 x^{3} + 20 x^{2}$

Step by step solution

Step1. Given Information

$The function is defined on (- \infty, \infty) and is differentiable at all points except at x = - 2 and x = 4 and that f^{'} (x) = 0 only at x = 0 and x = 5 .$

Step 2. Calculations

$The critical points of the function, therefore will be x = - 2; x = 0; x = 4; x = 5 Therefore, the differentiation of the function will be f^{'} (x) = x (x + 2) (x - 4) (x - 5) The graph can be drawn as$

$Therefore, the function is f (x) = 0.2 x^{5} - 1.75 x^{4} + 0.67 x^{3} + 20 x^{2}$

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Suppose that $f$ is defined on (−∞,∞) and differentiable everywhere except at $x = - 2$ and $x = 4$ , and that $f' (x) = 0$ only at $x = 0$ and $x = 5$ . 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 on (−∞,∞) and differentiable everywhere except at x=-2and x=4, and that f'(x)=0only at x=0and x=5. 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

Pure Maths

Mechanics Maths

Geometry

Discrete Mathematics

Applied Mathematics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Suppose that $f$ is defined on (−∞,∞) and differentiable everywhere except at $x = - 2$ and $x = 4$ , and that $f' (x) = 0$ only at $x = 0$ and $x = 5$ . List all the critical points of $f$ and sketch a possible graph of $f$ .