Question

The function f(x)=-2 x^{3}+30 x^{2}-144 x+11 has one local minimum and one local maximum. This function has a local minimum at x= and a local maximum at x= )

Answer 1

To find the local minimum and maximum points of the given function, take the derivative and set it equal to zero. Solve for x and plug the values back into the original function to get the y-values.

Step-by-step explanation:

The function f(x)=-2x^{3}+30x^{2}-144x+11 has one local minimum and one local maximum. To find these points, we need to take the derivative of the function and set it equal to zero.

First, let's find the derivative of the function. Taking the derivative, we get f'(x)=-6x^{2}+60x-144. Now, set f'(x)=0 and solve for x. Solving this equation will give us the x-coordinate of the local minima and maxima.

After finding the values of x, plug them back into the original function to get the corresponding y-values.