I need help with this problem: finding the instantaneous rate of change of y with respect to x at the point x=5 if y=x^2/2+3/5x-1
I know I am suppose to find the determinant first then plug in 5...but I am not sure about the determinant
You meant "derivative" instead of "determinant"
The determinant has nothing to do with this.
dy/dx = x + 3/5
when x = 5
dy/dx = 5 + 3/5 = 28/5 or 5.6
wait, what happened to the -1?
or the 2 in the x^2/2?
...wait, duh, i figured out the x^2/2
I assumed you knew how to find the derivative of such a simple expression.
Remember the derivative of a constant is zero ,
if you want I could write it as
dy/dx = x +3/4 + 0
ohh okay, i forgot about that! thank u so much for helping me :)
To find the instantaneous rate of change of y with respect to x at a specific point, you need to find the derivative of the function y with respect to x and then evaluate it at that point.
In this case, your function is y = (1/2)x^2 + (3/5)x - 1. To find the derivative, you can use the power rule and the constant rule.
The power rule states that if y = x^n, then dy/dx = nx^(n-1). Applying this rule, the derivative of (1/2)x^2 will be (1/2)*2x = x.
The derivative of (3/5)x is simply (3/5).
Since the derivative of a constant is 0, the derivative of -1 is 0.
Putting it all together, the derivative of y with respect to x, dy/dx, is x + (3/5).
Now, to find the instantaneous rate of change at the point x = 5, you can substitute x = 5 into the derivative function. So, dy/dx evaluated at x = 5 will be 5 + (3/5).
Therefore, the instantaneous rate of change of y with respect to x at the point x = 5 is 5 + (3/5).