Question

find the values of b such that the function has the given maximum value. (enter your answers as a comma-separated list.) f(x) = −x2 bx − 45; maximum value: 55

Answer 1

To find the values of b such that the function has the given maximum value, set the derivative of the function equal to zero and solve for b. Substituting the maximum value into the function, we find two possible values for b: 10 and -20.

Step-by-step explanation:

To find the values of b such that the function has the given maximum value, we need to set the derivative of the function equal to zero and solve for b. First, let's find the derivative of the function:

f'(x) = -2x - b

Setting the derivative equal to zero, we have:

-2x - b = 0

Solving for x, we get x = -b/2. Substituting this value back into the original function, we have:

f(x) = -(-b/2)^2 + b(-b/2) - 45

Now we can substitute the maximum value of 55 into the function and solve for b:

55 = -(-b/2)^2 + b(-b/2) - 45

Simplifying and solving the quadratic equation, we find two possible values of b: b = 10 or b = -20.