find the instantaneous rate of change of the function fx 13

find the instantaneous rate of change of the function f(x) = 13x2 + 19x + 27 at x = 16.

Solution

f(x) = 13x^2 + 19x + 27

to find the instantaneous rate of change let us differentiate the function with repect to x. we will use the rule d/dx(x^n) = nx^(n-1)

f\'(x) = 13*2x^(2-1) + 19*1x^(1-1) + 0

=> f\'(x) = 26x +19

Therefore instantaneous rate of change at x= 16 is

f\'(16) = 26*16 + 19 = 435