If f(x) = 7x³ – 3e², find: f'(z) = f'(4) = | f'"(x) = f''(4) =|

Calculus: Early Transcendentals
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ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Calculus Problem: Finding Derivatives

Given the function \( f(x) = 7x^3 - 3e^x \), find the following:

1. The first derivative of the function, denoted as \( f'(x) \).
2. The value of the first derivative at \( x = 4 \), denoted as \( f'(4) \).
3. The second derivative of the function, denoted as \( f''(x) \).
4. The value of the second derivative at \( x = 4 \), denoted as \( f''(4) \).

**Solution:**

To solve for these derivatives:

**1. First derivative \( f'(x) \):**
\[ f'(x) = \]

**2. Value of the first derivative at \( x = 4 \):**
\[ f'(4) = \]

**3. Second derivative \( f''(x) \):**
\[ f''(x) = \]

**4. Value of the second derivative at \( x = 4 \):**
\[ f''(4) = \]

Further steps involve applying differentiation rules to compute the derivatives and then substitute \( x = 4 \) to find the specific values.
Transcribed Image Text:### Calculus Problem: Finding Derivatives Given the function \( f(x) = 7x^3 - 3e^x \), find the following: 1. The first derivative of the function, denoted as \( f'(x) \). 2. The value of the first derivative at \( x = 4 \), denoted as \( f'(4) \). 3. The second derivative of the function, denoted as \( f''(x) \). 4. The value of the second derivative at \( x = 4 \), denoted as \( f''(4) \). **Solution:** To solve for these derivatives: **1. First derivative \( f'(x) \):** \[ f'(x) = \] **2. Value of the first derivative at \( x = 4 \):** \[ f'(4) = \] **3. Second derivative \( f''(x) \):** \[ f''(x) = \] **4. Value of the second derivative at \( x = 4 \):** \[ f''(4) = \] Further steps involve applying differentiation rules to compute the derivatives and then substitute \( x = 4 \) to find the specific values.
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