What is the instantaneous slope of y = negative 7 over x at x = 3?
y = -7/x or y = -7x^-1
dy/dx = 7x^-2 = 7/x^2
when x = 3
instantaneous slope = dy/dx = 7/9
Well, if you take the derivative of y = -7/x, you get y' = 7/x^2. At x = 3, the instantaneous slope would be 7/3^2, which is 7/9. So, the slope is going to be just a bit over 7, but not quite 8. It's like trying to be cool, but not quite making it. It's the almost-cool slope of 7/9.
To find the instantaneous slope of the curve y = -7/x at x = 3, we need to find the derivative of the function and evaluate it at x = 3.
First, let's find the derivative of y with respect to x.
Using the quotient rule, the derivative of y = -7/x is given by:
dy/dx = (d/dx)(-7) * x^(-1) - (-7) * (d/dx)(x^(-1))
= 0 * x^(-1) + 7 * (-1) * x^(-2)
= -7/x^2
Now, let's evaluate this derivative at x = 3:
dy/dx = -7/(3^2)
= -7/9
Therefore, the instantaneous slope of y = -7/x at x = 3 is -7/9.
To find the instantaneous slope of the function y = -7/x at x = 3, we need to take the derivative of the function and evaluate it at x = 3.
First, let's find the derivative of y with respect to x. The function y = -7/x can be rewritten as y = -7x^(-1).
To find the derivative, we need to use the power rule. The power rule states that the derivative of x^n with respect to x is nx^(n-1).
Using the power rule, the derivative of y = -7x^(-1) is:
dy/dx = -7 * -1 * x^(-1 - 1)
dy/dx = 7x^(-2)
Now that we have the derivative, let's find the instantaneous slope by evaluating it at x = 3. Substituting x = 3 into the derivative, we have:
dy/dx(x = 3) = 7(3)^(-2)
dy/dx(x = 3) = 7/9
Therefore, the instantaneous slope of y = -7/x at x = 3 is 7/9.