# How do you find the equation of the line tangent to the graph of #y=x^2# at the point x=1?

Find the slope by taking the derivative; use the slope and the point

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

To find the equation of the line tangent to the graph of y=x^2 at the point x=1, we can use the concept of differentiation.

First, we differentiate the function y=x^2 with respect to x to find its derivative. The derivative of y=x^2 is dy/dx = 2x.

Next, we substitute x=1 into the derivative to find the slope of the tangent line at x=1. When x=1, the slope is 2(1) = 2.

Now, we have the slope of the tangent line, which is 2, and the point of tangency, which is (1, 1) since x=1.

Using the point-slope form of a linear equation, y - y1 = m(x - x1), we can substitute the values into the equation.

Therefore, the equation of the line tangent to the graph of y=x^2 at the point x=1 is y - 1 = 2(x - 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 instantaneous velocity at #t=2# for the position function #s(t) = t^3 +8t^2-t#?
- What is the equation of the normal line of #f(x)= x+x/(1+x/(1+1/x))# at #x = 1#?
- What is the instantaneous rate of change of #f(x)=-2x^3-8x^2-x # at #x=2#?
- How do you use the limit definition of the derivative to find the derivative of #f(x)=4/(x-3)#?
- What is the equation of the line that is normal to #f(x)= ln(sin^2x) # at # x=(4pi)/3 #?

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