Whats the slope of the tangent to the curve y=7/(square root of x) at the point where x=a>0?
To find the slope of the tangent to the curve at a given point, we need to take the derivative of the curve equation and evaluate it at that specific point.
Let's start by finding the derivative of the curve:
y = 7 / √x
To simplify the process, we can rewrite the equation as:
y = 7x^(-1/2)
Now, we can apply the power rule for differentiation, which states that if we have a function of the form f(x) = ax^n, the derivative is given by:
f'(x) = anx^(n-1)
Using the power rule on our curve equation:
y' = (-1/2) * 7x^(-1/2 - 1)
Simplifying further:
y' = -7/2 * x^(-3/2)
Now, to find the slope of the tangent at x = a, substitute a into the derivative equation:
slope of the tangent = -7/2 * a^(-3/2)
Therefore, the slope of the tangent to the curve y = 7/√x at the point x = a is -7/2 * a^(-3/2).