8x^3+2x^2-8 estimate the relative maxima and relative minima

Compute the derivative:



Set equal to zero and find the critical points:



Compute the second derivative at the critical points to determine concavity. If the second derivative is positive, the function is concave upward at that point, so the function attains a minimum at the critical point. If negative, the critical point is the site of a maximum.



At , the second derivative takes on the value of , so the function is concave upward, so the function has a minimum there of .

At , the second derivative is , so the function is concave downward and has a maximum there of .

C+19÷-17=17c+(-1.11764706)=17c=.11764706)c=18.1176471