Question

The slope of the function \( f(x) = 2x^4 - 3x^2 + 5x \) at \( x = 2 \) is _____. \(\textit{[Answer in integer.]}\)

Hint:

The slope of a function at a given point is simply the value of its derivative at that point.

Answer 1

Correct Answer: 57

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 \( \boxed{57} \).