Question

On the curve y = x², 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

The slope of the curve y = x² at point P (2, 8) is found by taking the derivative, which results in a slope of 4. This slope is found by substituting x = 2 into the derivative dy/dx = 2x.

Step-by-step explanation:

The slope of the curve y = x² at a given point can be found by taking the derivative of y with respect to x, which gives us the slope of the tangent line at that point. So, the derivative of y = x² is dy/dx = 2x. At point P, which has coordinates (2, 8), we substitute x = 2 into the derivative to find the slope at that point. This gives us 2 * 2 = 4, which means the slope of the curve at point P is 4. Thus, the closest answer given (although not exact in this question's context) would be (a) 16 if it were misprinted and should have been 4, or b) 13 if we are considering the nearest options provided.

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