What is the second derivative of f(x) = 2x^4 - 3x^3 + x?
Practice Questions
1 question
Q1
What is the second derivative of f(x) = 2x^4 - 3x^3 + x?
24x^2 - 18x + 1
24x^2 - 9
12x^2 - 9
8x^3 - 9
First derivative f'(x) = 8x^3 - 9x^2 + 1. Second derivative f''(x) = 24x^2 - 18x.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the second derivative of f(x) = 2x^4 - 3x^3 + x?
Solution: First derivative f'(x) = 8x^3 - 9x^2 + 1. Second derivative f''(x) = 24x^2 - 18x.
Steps: 7
Step 1: Start with the function f(x) = 2x^4 - 3x^3 + x.
Step 2: To find the first derivative f'(x), use the power rule. For each term, multiply the coefficient by the exponent and decrease the exponent by 1.
Step 3: Apply the power rule to each term: For 2x^4, the derivative is 8x^3; for -3x^3, the derivative is -9x^2; and for x, the derivative is 1.
Step 4: Combine the results to get the first derivative: f'(x) = 8x^3 - 9x^2 + 1.
Step 5: Now, find the second derivative f''(x) by differentiating f'(x) again using the power rule.
Step 6: Apply the power rule to each term of f'(x): For 8x^3, the derivative is 24x^2; for -9x^2, the derivative is -18x; and the derivative of 1 is 0.
Step 7: Combine the results to get the second derivative: f''(x) = 24x^2 - 18x.
