Question

The function f(x)=x4−9x3+23x has a critical point at x=1. Use the second derivative test to identify it as a local maximum or local minimum. f(x) has a local maximum at x=1. f(x) has a local minimum at x=1.

Answer 1

Answer:

x = 1 is a local maxima

Step-by-step explanation:

Let us start by finding the first and second derivatives of this function

$f(x) = x^{4} -9x^{3}+23x\\f'(x) = 4x^{3}-27x^{2}  +23\\f''(x) = 12x^{2} -54x$

Now let's find the value of the second derivative at x=1.

$f''(1) = 12(1)^{2} -54(1) = -42$

So the second derivative is negative which means that there is a local maxima at x = 1