How do you find instantaneous rate of change for the equation y=4x^3+2x-3?

1 Answer
Nov 25, 2016

Take the derivative: " "12x^2 + 2

Explanation:

The rate of change for an equation may simply be defined mathematically as the slope at any point.

if f(x) = 4x^3 + 2x -3 then

f'(x) = 12x^2 + 2 using the power rule from calculus.

For each polynomial term, multiply the exponent times the coefficient and decrease the exponent by one.

Thus for f'(x), 4x^3 becomes (3 xx 4) x^(3-1) = 12x^2 (power rule)

f'(x) for 2x becomes (1 xx 2)x^(1-1) = 2

f'(x) for -3 becomes (0 xx 3) = 0

Combine the terms (sum rule): 12x^2 + 2.