Question

Calculus!

On the curve y = x^3, point P has the coordinates (2, 8). What is the slope of the curve at point P?
A.
16
B.
13
C.
12
D.
11

Answer 1

C. 12

Step-by-step explanation:

The function is y = x³

The slope of the function at any point (x, y) is found by computing the first derivative of the function

f'(x) = d/dx(f(x)) = d/dx(x³) = 3x² using d/dx(xᵃ) = axᵃ⁻1

At x = 2, f'(x) = f'(z) = 3(2)² = 3 x 4 = 12

Answer: Option C : 12