61.2k views
3 votes
Let f(x) = 2x² - 16x - 7. a. Find the values of x for which the slope of the curve y = f(x) is 0. b. Find the values of x for which the slope of the curve y = f(x) is 4. a.

User Sreenavc
by
7.9k points

1 Answer

2 votes

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.

User Simone Chelo
by
7.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories