Find the instantaneous rate of change when x = 3 given the function g(x) = 5x^2 + 6x.
My answer:
g'(x) = 10x + 6
10(3)+6 = 36
g'=10x+6 when x=3, g'=36
To find the instantaneous rate of change when x = 3 for the function g(x) = 5x^2 + 6x, we need to find the derivative of g(x), denoted as g'(x). Taking the derivative of g(x), we get:
g'(x) = 10x + 6
Now, to find the instantaneous rate of change at x = 3, we substitute x = 3 into the derivative function:
g'(3) = 10(3) + 6
g'(3) = 30 + 6
g'(3) = 36
Therefore, the instantaneous rate of change when x = 3 is 36.
To find the instantaneous rate of change, we need to calculate the derivative of the function g(x).
Given the function g(x) = 5x^2 + 6x, we can find its derivative by applying the power rule for derivatives. The power rule states that for any term of the form ax^n, the derivative is given by nx^(n-1).
Using the power rule, we differentiate each term of g(x) separately. The derivative of 5x^2 with respect to x is 10x, and the derivative of 6x with respect to x is simply 6.
Therefore, g'(x) = 10x + 6.
To find the instantaneous rate of change when x = 3, we substitute x = 3 into the derivative equation:
g'(3) = 10(3) + 6
= 30 + 6
= 36.
Therefore, the instantaneous rate of change of g(x) when x = 3 is 36.