Find the slope m of the tangent to the curve
y = 3/√ x at the point where x = a > 0
y = 2x^(-1/2)
dy/dx = -x^(-3/2)
= -1/(√x)^3
so for x = a , a>0
dy/dx = -1/(√a)^3
good math, bad reading. :-(
Oh well, 2 or 3 , close enough.
blame it on "oldsheimers"
To find the slope of the tangent to the curve at a specific point, we need to find the derivative of the function with respect to x and then evaluate it at that point.
The given equation is y = 3/√x. To find the derivative, we can use the power rule for differentiation. The power rule states that if we have a function of the form y = x^n, where n is a constant, then the derivative of that function is given by dy/dx = nx^(n-1).
Applying the power rule to our function y = 3/√x, we can rewrite it as y = 3x^(-1/2). Now we can find the derivative dy/dx by applying the power rule:
dy/dx = (-1/2) * 3 * x^(-1/2 - 1)
= (-3/2) * x^(-3/2 - 2/2)
= (-3/2) * x^(-5/2)
Now we have the derivative of the function. To find the slope of the tangent at the point x = a, we substitute a into the derivative we just found:
m = (-3/2) * a^(-5/2)
Therefore, the slope of the tangent to the curve y = 3/√x at the point where x = a is (-3/2) * a^(-5/2).