Use the four-step process to find the slope of the tangent line to the graph of the given function at any point.

A)

Question

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. ​
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A) ​

Quizplus · Accepted Answer

Step 1: Given function is f(x) = x^2 + 2x - 3.

Step 2: We need to find the derivative of the given function.

f'(x) = 2x + 2

Step 3: We need to find the slope of the tangent line at any point, which is the value of the derivative at that point.

Let's choose the point (1, 0).

f'(1) = 2(1) + 2 = 4

Therefore, the slope of the tangent line at the point (1, 0) is 4.

Step 4: The final answer is the equation of the tangent line passing through the point (1,0) with slope 4.

y - 0 = 4(x - 1)

y = 4x - 4

Therefore, the equation of the tangent line at the point (1,0) is y = 4x - 4.

Option C is the correct choice, as it matches the equation of the tangent line we found.

Use the Four-Step Process to Find the Slope of the Tangent