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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Answer to a math 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.
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.
Frequently asked questions (FAQs)
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