How do you find the equation of the tangent line to the graph of #f(x)=x^3+1# at point (1,2)?

Answer 1

The derivative of #f(x)# is given by the power rule, which states that #d/dx(x^n) = nx^(n -1)#. .

#f'(x) = 3x^(3 - 1) + 0(1)x^(0 - 1)#

#f'(x) = 3x^2#

We now determine the slope of the tangent line by plugging in the point #x =a# into the derivative.

#f'(1) = 3(1)^2 = 3#

Now we can readily find the equation of the line.

#y -y_1 = m(x - x_1)#

#y - 2 = 3(x - 1)#

#y = 3x - 3 + 2#

#y = 3x - 1#

Now we can check the graphical interpretation and confirm that we are correct.

Hopefully this helps!

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

To find the equation of the tangent line to the graph of f(x)=x^3+1 at point (1,2), we need to find the slope of the tangent line at that point. The slope of the tangent line is equal to the derivative of the function evaluated at x=1. Taking the derivative of f(x)=x^3+1, we get f'(x)=3x^2. Evaluating f'(x) at x=1, we find f'(1)=3(1)^2=3. Therefore, the slope of the tangent line is 3.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values x1=1, y1=2, and m=3 into the equation. This gives us y - 2 = 3(x - 1). Simplifying, we get y - 2 = 3x - 3. Rearranging the equation, we have y = 3x - 1.

Therefore, the equation of the tangent line to the graph of f(x)=x^3+1 at point (1,2) is y = 3x - 1.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7