graph

[Mickey]

What would the graph be of a function with a local maximum at x = -2 a local maximum at x = 6 and a local minimum at x = 1
Can we conclude that since there are 2 maxima, then it must be an expression with something to the 4th power?

 

[skeeter]

What would the graph be of a function with a local maximum at x = -2 a local maximum at x = 6 and a local minimum at x = 1
Can we conclude that since there are 2 maxima, then it must be an expression with something to the 4th power?

it could be a 4th degree polynomial.

A 4th degree polynomial with derivative ...

\(\displaystyle y' = -(x+2)(x-1)(x-6)\)

... would be a good start.

 

[fasteddie65]

You might try inserting a constant, like "a", as a coefficient in the derivative equation.

 

[soroban]

Hello, Mickey!

What would the graph be of a function with a local maximum at x = -2, a local maximum at x = 6,
and a local minimum at x = 1?
Can we conclude that since there are 2 maxima, then it must be an expression
with something to the 4th power?

If the graph has exactly two maximums and one minimum, you are correct.
. . The graph is M-shaped: \(\displaystyle /\backslash/\backslash\)

Otherwise, skeeter is correct.
. . There could be other maxima and minima.