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

The derivative of

#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

#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!

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

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.

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

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.

- How do you find the slope of the secant lines of #f(x) = (1/x) # through the points: (-4,(f(-4)) and (1,f(1))?
- How do you find the derivative of # F(x)=x^3−7x+5# using the limit definition?
- How do you use the limit definition to find the slope of the tangent line to the graph #F(x) = (( x^2) – 9) # at (2, -5)?
- What is the equation of the tangent line of #f(x) =tan^3x/x# at #x=pi/4#?
- What is the slope of the line normal to the tangent line of #f(x) = cscx-sin2x # at # x= (pi)/12 #?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7