Question

The Function F(X)=−2x3+33x2−60x+7 Has One Local Minimum And One Local Maximum.

This Function Has A Local Minimum At X=
And A Local Maximun at X =

Answer 1

The function f(x) = -2x^3 + 33x^2 - 60x + 7 has a local minimum at x = 1 and a local maximum at x = 10.

Step-by-step explanation:

The function f(x) = -2x^3 + 33x^2 - 60x + 7 has one local minimum and one local maximum.

To find the local minimum and maximum, we can use calculus. First, we take the derivative of the function and set it equal to zero to find the critical points.

f'(x) = -6x^2 + 66x - 60 = 0

Solving this quadratic equation, we find that x = 1 and x = 10 are the critical points.

Next, we take the second derivative of the function and evaluate it at the critical points to determine whether each point is a local minimum or maximum.

f''(x) = -12x + 66

At x = 1, f''(1) = 54, which is positive, so it is a local minimum. At x = 10, f''(10) = -54, which is negative, so it is a local maximum.

Therefore, the function has a local minimum at x = 1 and a local maximum at x = 10.