Differentiating exponential functions in exercise, find the derivative of the function.
y = 4e(x)^1/2

.

Step-by-step explanation:

Properties of derivative :

Given function :

Now , differentiate both sides of the above equation with respect to x , we get

 (Using(2))

  (Using  (1))

Hence, the derivative of the given function is .

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this