Final answer:
The values of x for which the slope of the curve y = f(x) is zero is x = 4, and the value of x for which the slope is 4 is x = 5. These values were found by calculating and setting the derivative f'(x) = 4x - 16 equal to 0 and 4, respectively.
Step-by-step explanation:
To find the values of x for which the slope of the curve y = f(x) is zero, we calculate the derivative of the function f(x) = 2x² - 16x - 7 and set it equal to zero. The derivative f'(x) represents the slope of the curve at any point x. So, we need to solve f'(x) = 0.
Step 1: Find the derivative of f(x): f'(x) = 4x - 16.
Step 2: Set f'(x) to zero and solve for x:
4x - 16 = 0
x = 4.
The value of x for which the slope of the curve is zero is x = 4.
To find the values of x for which the slope of the curve y = f(x) is 4, we set the derivative equal to 4 and solve for x:
Step 1: Use the derivative found earlier: f'(x) = 4x - 16.
Step 2: Set f'(x) to 4 and solve for x:
4x - 16 = 4
x = 5.
The value of x for which the slope of the curve is 4 is x = 5. Therefore, the answers are x = 4 for part a and x = 5 for part b.