Let y= f(x) = 3 - x^4 Find the increment in y, △y, when x changes from 0.4 to 1.3.

Question

Let y= f(x) = 3 - x⁴ Find the increment in y, △y, when x changes from 0.4 to 1.3.

Answer 1

To find this change in y,  △y, simply evaluate the function at both x = 0.4 and x = 1.3, then subtract the former from the latter.

f(0.4) = 3 - (0.4)⁴ = 2.9744

f(1.3) = 3 - (1.3)⁴ = 0.1439

△y = f(1.3) - f(0.4) = 0.1439 − 2.9744 = −2.8305. As a sanity check, the fact that this number is negative should make sense since f(x)'s dominant term is -x⁴, which is strictly decreasing from the point x=0 onward.