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Question
Math
Posted 3 months ago
very clear steps
Determine the second derivative of the function f(x)=3x32x2+4xf(x) = 3x^3 - 2x^2 + 4x.
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Answer from Sia
Posted 3 months ago
Solution by Steps
step 1
To find the second derivative of the function f(x)=3x32x2+4x f(x) = 3x^3 - 2x^2 + 4x , we first differentiate f(x) f(x) with respect to x x to get f(x) f'(x)
step 2
Differentiating f(x) f(x) gives us f(x)=9x24x+4 f'(x) = 9x^2 - 4x + 4
step 3
We then differentiate f(x) f'(x) to get the second derivative f(x) f''(x)
step 4
Differentiating f(x) f'(x) gives us f(x)=18x4 f''(x) = 18x - 4
Answer
The second derivative of the function f(x)=3x32x2+4x f(x) = 3x^3 - 2x^2 + 4x is f(x)=18x4 f''(x) = 18x - 4 .
Key Concept
Second Derivative
Explanation
The second derivative of a function is the derivative of the derivative, which provides information about the curvature of the function's graph.

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