Question

Is `f(x)=x^3+2x-4` increasing or decreasing at `x=0`?

Answer 1

increasing.

Explanation:

first we have to find `fprime(x)`
now,
`fprime(x)`
`=d/(dx){f(x)}`
`=d/(dx)(x^3+2x-4)`
`=d/(dx)(x^3)-2(d)/(dx)(x)-d/(dx)(4)`
`=3x^2+2-0`
now, putting the value `x=0` in `fprime(x)`,
`fprime(0)`
`=3(0)^2+2-0`
`=0+2-0`
`=2`
so, `fprime(0)=2`
`2>0`
we know, if the value of first derivative of a function in a point is greater than `0` , then the function is increasing at that point.
so, `f(x)` is increasing at `x=0` point