Question

Find the instantaneous rate of change for the function at the gi.

g(x)=x²+11x-15 at x=1

A)11
B)26
C)13
D)-9

Answer 1

To find the instantaneous rate of change for the function at x=1, we find the derivative of the function g(x)=x²+11x-15 and plug in x=1. The derivative of g(x) is 2x+11, and plugging in x=1 gives us an instantaneous rate of change of 13.

Step-by-step explanation:

To find the instantaneous rate of change for the function at x=1, we need to find the derivative of the function. The function g(x)=x²+11x-15 can be written as g(x)=x²+11x-15. To find the derivative, we take the derivative of each term separately. The derivative of x² is 2x, the derivative of 11x is 11, and the derivative of -15 is 0. Therefore, the derivative of g(x) is 2x+11.

Now, we can find the instantaneous rate of change by plugging in x=1 into the derivative. So, plugging in x=1, we get 2(1)+11=13. Therefore, the instantaneous rate of change for the function at x=1 is 13.