Q. 44 Use the first derivative test to... [FREE SOLUTION]

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Chapter 3: Q. 44 (page 261)

Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility. $f (x) = e^{x} (x^{2} - x - 1)$

Short Answer

Expert verified

Ans: The local maximum of the function f(x) is $x = - 2$

The local minimum of the function f(x) is $x = 1$

Step by step solution

Step 1. Given Information:

$f (x) = e^{x} (x^{2} - x - 1)$

Step 2. Finding the derivative of the function:

$f (x) = e^{x} (x^{2} - x - 1) f' (x) = e^{x} (2 x - 1) + (x^{2} - x - 1) e^{x} f' (x) = e^{x} (2 x - 1 + x^{2} - x - 1) f' (x) = e^{x} (x^{2} + x - 2) l e t, f' (x) = 0 鈭� e^{x} (x^{2} + x - 2) = 0 \begin{array}{r} x^{2} + x - 2 = 0 \\ x^{2} + 2 x - x - 2 = 0 \\ x (x + 2) - (x + 2) = 0 \\ (x + 2) (x - 1) = 0 \end{array} x = - 2, 1 t h e c r i t i c a l p o i n t s a r e x = - 2, 1$

Step 3. Substituting the values into the function equation:

$f (- 2) = e^{(- 2)} ({(- 2)}^{2} - (- 2) - 1) = e^{- 2} (4 + 2 - 1) = 5 e^{- 2} f (1) = e^{(1)} ({(1)}^{2} - (1) - 1) = - e 鈭� t h e l o c a l m a x i m u m a t x = - 2; a n d t h e l o c a l m i m i m u m a t x = 1$

Step 4. Verifying algebraic answers with graphs :

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91影视

Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility. $f (x) = e^{x} (x^{2} - x - 1)$

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Finding the derivative of the function:

Step 3. Substituting the values into the function equation:

Step 4. Verifying algebraic answers with graphs :

One App. One Place for Learning.

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91影视

Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility.f(x)=ex(x2-x-1)

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Finding the derivative of the function:

Step 3. Substituting the values into the function equation:

Step 4. Verifying algebraic answers with graphs :

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Decision Maths

Geometry

Study anywhere. Anytime. Across all devices.

Use the first derivative test to determine the local extrema of each function in Exercises 39- 50. Then verify your algebraic answers with graphs from a calculator or graphing utility. $f (x) = e^{x} (x^{2} - x - 1)$