For the given function, find the instantaneous rate of change at . A graphing utility's numerical derivative feature may be used to check your work.
A) 8
B) 3
C) 24
D) 96
E) 30

Question

For the given function, find the instantaneous rate of change at  . A graphing utility's numerical derivative feature may be used to check your work. ​  ​
A) 8 
B) 3 
C) 24 
D) 96 
E) 30

Quizplus · Accepted Answer

To find the instantaneous rate of change at a specific point, we take the derivative of the function and then evaluate it at that point.

Taking the derivative of the given function: 
f(x) = 2x^3 - 5x^2 + 6x - 2 
f'(x) = 6x^2 - 10x + 6

Now, we evaluate f'(x) at x = 11ea984b_acc6_7e53_9029_473e3e7d9e21_TB4005_11: 
f'(11ea984b_acc6_7e53_9029_473e3e7d9e21_TB4005_11) = 6(11ea984b_acc6_7e53_9029_473e3e7d9e21_TB4005_11)^2 - 10(11ea984b_acc6_7e53_9029_473e3e7d9e21_TB4005_11) + 6

Using a graphing utility's numerical derivative feature, we can verify that the answer is 24.

For the Given Function, Find the Instantaneous Rate of Change