Question
Find the x -coordinates of all relative maxima of f(x) - f(x)=3x^3+45x^2+81x+11 Answer Attempt 1 out of 4 x=
Solution
4.5
(239 Votos)
Carlos
Profissional · Tutor por 6 anos
Resposta
To find the x-coordinates of all relative maxima of the function
, we need to find the critical points of the function and then determine which of these points correspond to relative maxima.Step 1: Find the derivative of the function
.The derivative of
is given by:
Step 2: Set the derivative equal to zero and solve for
.
Step 3: Determine the second derivative of the function
.The second derivative of
is given by:
Step 4: Evaluate the second derivative at the critical point
.
Since
, the critical point
corresponds to a relative maximum.Therefore, the x-coordinate of the relative maximum of the function
is
.