Question

How do you find local maximum value of f using the first and second derivative tests: `f(x) = 7e^x`?

Answer 1

`If a < b and x in [a, b], minf(x) = 7e^a and max f(x) = 7e^b`

Explanation:

The function remains the same upon differentiation, any number of times. This is a characteristic of `e^x`.
For all x, `e^x >0`. So are the derivatives.
`d/dxf(x)>0`. So, `7e^x` is an increasing function, from 0 to infinity. through 7 at x = 0..