Question:
The slope of the function \( f(x) = 2x^4 - 3x^2 + 5x \) at \( x = 2 \) is _____. \(\textit{[Answer in integer.]}\)
The slope of the function \( f(x) = 2x^4 - 3x^2 + 5x \) at \( x = 2 \) is _____. \(\textit{[Answer in integer.]}\)
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The slope of a function at a given point is simply the value of its derivative at that point.
Updated On: Nov 27, 2025
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Correct Answer: 57
Solution and Explanation
To find the slope, we need to compute the derivative of the function:
\[
f'(x) = \frac{d}{dx}(2x^4 - 3x^2 + 5x) = 8x^3 - 6x + 5
\]
Substitute \( x = 2 \):
\[
f'(2) = 8(2^3) - 6(2) + 5 = 8(8) - 12 + 5 = 64 - 12 + 5 = 57
\]
Thus, the slope at \( x = 2 \) is \( \boxed{57} \).
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