`f(x) = e^x - x^3` Find the first and second derivatives of the function. Check to see that your answers aer reasonable by comparing the graphs of f, f', and f''

Textbook Question

Chapter 3, 3.1 - Problem 46 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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nees101 | Student, Graduate | (Level 2) Adjunct Educator

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Given function is:


Now we will find the first derivative:




The second derivative is obtained by taking the derivative of the first derivative.




Comparison of graphs of f,f' and f'' is shown below:

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a-maths-9's profile pic

a-maths-9 | Middle School Teacher | (Level 1) Adjunct Educator

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now we will find 2nd derivative




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hkj1385 | (Level 1) Assistant Educator

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1) If f(x) = e^(nx) ; where n = a real number;

then f'(x) = n*e^(nx)

2) If f(x) = x^n ; where n = a real number

then f'(x) = n*x^(n-1)

Now, given f(x) = (e^x) -  (x^3)

Thus, f'(x) = (e^x) - 3*(x^2)

f"(x) = (e^x) - 6*(x^1) 

or, f"(x) = (e^x) - 6x

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