Question

Math

Posted 3 months ago

very clear steps

`Determine the second derivative of the function $f(x) = 3x^3 - 2x^2 + 4x$.`

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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

To find the second derivative of the function $f(x) = 3x^3 - 2x^2 + 4x$, we first differentiate $f(x)$ with respect to $x$ to get $f'(x)$

step 2

Differentiating $f(x)$ gives us $f'(x) = 9x^2 - 4x + 4$

step 3

We then differentiate $f'(x)$ to get the second derivative $f''(x)$

step 4

Differentiating $f'(x)$ gives us $f''(x) = 18x - 4$

Answer

The second derivative of the function $f(x) = 3x^3 - 2x^2 + 4x$ is $f''(x) = 18x - 4$.

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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