Find the slope of the tangent line to f(x) = 2x^3 - 3x^2 + 4 at x = 1. (2021)

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Question: Find the slope of the tangent line to f(x) = 2x^3 - 3x^2 + 4 at x = 1. (2021)

Options:

Correct Answer: 2

Solution:

f\'(x) = 6x^2 - 6. f\'(1) = 6(1)^2 - 6 = 0.

Find the slope of the tangent line to f(x) = 2x^3 - 3x^2 + 4 at x = 1. (2021)

Find the slope of the tangent line to f(x) = 2x^3 - 3x^2 + 4 at x = 1. (2021)

Step 1: Identify the function f(x) = 2x^3 - 3x^2 + 4.
Step 2: Find the derivative of the function, which gives us the slope of the tangent line. The derivative f'(x) is calculated as follows: f'(x) = d/dx(2x^3) - d/dx(3x^2) + d/dx(4).
Step 3: Calculate the derivative: f'(x) = 6x^2 - 6.
Step 4: Substitute x = 1 into the derivative to find the slope at that point: f'(1) = 6(1)^2 - 6.
Step 5: Calculate f'(1): f'(1) = 6(1) - 6 = 0.
Step 6: The slope of the tangent line to the function at x = 1 is 0.

Differentiation – The process of finding the derivative of a function, which gives the slope of the tangent line at any point.
Evaluating Derivatives – Substituting a specific value into the derivative to find the slope of the tangent line at that point.