To estimate the slope of the curve at x = 1, we can use the derivative.
The derivative of the function y = x^3 + 2 can be found by taking the derivative of each term separately.
The derivative of x^3 is 3x^2, and the derivative of 2 is 0 (since it is a constant).
Therefore, the derivative of y = x^3 + 2 is dy/dx = 3x^2.
To find the slope at x = 1, we substitute x = 1 into the derivative:
dy/dx = 3(1)^2
= 3
Therefore, the slope of the curve y = x^3 + 2 at x = 1 is 3.
Estimate the slope of the curve y = x ^ 3 + 2 at x = 1
1 answer