If y = 4x^2 + 3x + 2, find dy/dx at x = -1.

₹0.0

Question: If y = 4x^2 + 3x + 2, find dy/dx at x = -1.

Options:

Correct Answer: -5

Solution:

dy/dx = 8x + 3. At x = -1, dy/dx = 8(-1) + 3 = -8 + 3 = -5.

If y = 4x^2 + 3x + 2, find dy/dx at x = -1.

If y = 4x^2 + 3x + 2, find dy/dx at x = -1.

Correct Answer: -5

Step 1: Identify the function given, which is y = 4x^2 + 3x + 2.
Step 2: Differentiate the function with respect to x to find dy/dx. The derivative of 4x^2 is 8x, and the derivative of 3x is 3. The constant 2 has a derivative of 0.
Step 3: Combine the derivatives to get dy/dx = 8x + 3.
Step 4: Substitute x = -1 into the derivative. So, dy/dx = 8(-1) + 3.
Step 5: Calculate 8(-1) which equals -8, then add 3 to get -8 + 3.
Step 6: The final result is -5.

Differentiation – The process of finding the derivative of a function, which represents the rate of change of the function with respect to its variable.
Polynomial Functions – Understanding how to differentiate polynomial functions, which are functions of the form ax^n.
Substitution – Evaluating the derivative at a specific point by substituting the value of x into the derivative.