Question

What’s the slope of a tangent line at x=1 for f(x)=x2. We can find the slopes of a sequence of secant lines that get closer and closer to the tangent line. What we are working towards is the process of finding a “limit” which is a foundational topic of calculus.

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Fred

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To find the slope of the tangent line at x=1 for the function f(x)=x^2, we need to find the derivative of the function with respect to x.

The derivative of f(x)=x^2 can be found using the power rule, which states that the derivative of x^n (where n is any constant) is nx^(n-1).

Applying the power rule, we differentiate f(x)=x^2 as follows:

f'(x) = 2x^(2-1)

= 2x

Now, to find the slope of the tangent line at x=1, we substitute x=1 into the derivative function:

f'(1) = 2(1)

= 2

Therefore, the slope of the tangent line at x=1 for f(x)=x^2 is 2.

Answer: The slope of the tangent line at x=1 for f(x)=x^2 is 2.

The derivative of f(x)=x^2 can be found using the power rule, which states that the derivative of x^n (where n is any constant) is nx^(n-1).

Applying the power rule, we differentiate f(x)=x^2 as follows:

f'(x) = 2x^(2-1)

= 2x

Now, to find the slope of the tangent line at x=1, we substitute x=1 into the derivative function:

f'(1) = 2(1)

= 2

Therefore, the slope of the tangent line at x=1 for f(x)=x^2 is 2.

Answer: The slope of the tangent line at x=1 for f(x)=x^2 is 2.

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