Question

On the curve y=x^2+x, point p has the coordinates (1.2,2.64). Estimate the slope of the curve at point p by taking values very close the the x coordinate of P.

Answer 1

Explanation:

Two close values I will use are x = 1.19 and x = 1.21

Value of the function at x = 1.19 = 2.6061

x = 1.21 = 2.6741

Rise / run = slope = (2.6741-2.6061) / (1.21 - 1.19) = 3.4 approx

The actual slope ....found by subbing in thpoint to the derivtive of the function :

slope = f'(x) = 2x +1

2(1.2) +1 = 3.4 so the approximate solution was 'spot on' !