I am having trouble with this problem :
Find k such that the line is tangent to the graph of the function.
Function : f(x)=k√x
Line : y = 4x + 4
If we take the derivative of our function, what do we get? Well, our derivative is the slope of the tangent to the curve at any given point.
From our line, we know the slope is 4! What can we do with this information, well we now have
$\displaystyle f`(x) = \frac{k}{2 \sqrt{x} } = 4 $
This is one condition, but we also have the condition that the line must intersect our function! So we have,
$\displaystyle 4x + 4 = k \sqrt{x} $
Well, now we have 2 equations with 2 unknowns! Solve for K and you have your answer.