posted by jenny on .
The function f(x)= (8x-7)e^2x has one critical number. Find it
A critical point in the domain of x is a value of x at which the function is not differentiable or where the derivative is zero.
For the case in point:
f'(x) can be found using the product rule and the chain rule as
Setting f'(x)=0 and solving for x, we get e^2x=0 or x=3/8.
Since the range of e^2x excludes 0, it is a solution to be rejected. So the unique point required is x=3/8.