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Use calculus to sketch the graph of the given function. (a) f(x) = 3x* – 4x³ %3D | (b) f(x) = 3xª – 8x³ + 6x² + 2 - (c) f(x) = 3– (x+1)³ (d) f(x) = 2x³ + 6x² + 6x +5

Use calculus to sketch the graph of the given function. (a) f(x) = 3x* – 4x³ %3D | (b) f(x) = 3xª – 8x³ + 6x² + 2 - (c) f(x) = 3– (x+1)³ (d) f(x) = 2x³ + 6x² + 6x +5

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 42E
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Use calculus to sketch the graph of the given function. (a) f(x) = 3x* – 4x³ (b) f(x) = 3x* – 8r° + 6x² +2 (c) f(x) = 3 – (x +1)³ (d) f(x) = 2x³ + 6x² + 6x +5 %3D %3D (e) f(x) = x³ (x +5)²
Transcribed Image Text:Use calculus to sketch the graph of the given function. (a) f(x) = 3x* – 4x³ (b) f(x) = 3x* – 8r° + 6x² +2 (c) f(x) = 3 – (x +1)³ (d) f(x) = 2x³ + 6x² + 6x +5 %3D %3D (e) f(x) = x³ (x +5)²
1. Get the first derivative f': 2. Find the factors: 3. Find the critical numbers: 4. Get the second derivative f": 5. Find the factors: 6. Find the critical numbers: 7. Draw a number line and plot (not to scale) all the critical numbers arranged in as- cending order: 8. Make the table similar to what is shown below. Create rows for the intervals and critical numbers. 9. Choose values of c from the intervals: 10. Compute the function values for the critical numbers: 11. Note f'(x) = 0 for x = -},1 and f"(x) = 0 for x = -3,1. Write 0 accordingly. 12. Fill out other values for the column for f' and f". Exact values can be provided but the SIGNS are already sufficient and more important. 13. Draw conclusions 14. Sketch the graph.
Transcribed Image Text:1. Get the first derivative f': 2. Find the factors: 3. Find the critical numbers: 4. Get the second derivative f": 5. Find the factors: 6. Find the critical numbers: 7. Draw a number line and plot (not to scale) all the critical numbers arranged in as- cending order: 8. Make the table similar to what is shown below. Create rows for the intervals and critical numbers. 9. Choose values of c from the intervals: 10. Compute the function values for the critical numbers: 11. Note f'(x) = 0 for x = -},1 and f"(x) = 0 for x = -3,1. Write 0 accordingly. 12. Fill out other values for the column for f' and f". Exact values can be provided but the SIGNS are already sufficient and more important. 13. Draw conclusions 14. Sketch the graph.
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