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Question
Find the rate at which the function f (x) = x4 − 2x3 + 3x2 + x + 5 changes with respect to x.
Solution
\[ = \frac{d}{dx}\left( x^4 - 2 x^3 + 3 x^2 + x + 5 \right)\]
\[ = \frac{d}{dx}\left( x^4 \right) - 2\frac{d}{dx}\left( x^3 \right) + 3\frac{d}{dx}\left( x^2 \right) + \frac{d}{dx}\left( x \right) + \frac{d}{dx}\left( 5 \right)\]
\[ = 4 x^3 - 2\left( 3 x^2 \right) + 3\left( 2x \right) + 1 + 0\]
\[ = 4 x^3 - 6 x^2 + 6x + 1\]
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