How do you find the equation of the line tangent to the graph of #y = x^2 - 3# at the point P(2,1)?
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 - 3 at the point P(2,1), we can use the concept of differentiation.
First, we differentiate the given function y = x^2 - 3 with respect to x to find its derivative.
The derivative of y = x^2 - 3 is dy/dx = 2x.
Next, we substitute the x-coordinate of the point P(2,1) into the derivative to find the slope of the tangent line at that point.
Substituting x = 2 into dy/dx = 2x, we get the slope m = 2(2) = 4.
Now, we have the slope of the tangent line, and we also have a point on the line, P(2,1). We can use the point-slope form of a linear equation to find the equation of the tangent line.
Using the point-slope form, y - y1 = m(x - x1), where (x1, y1) is the point (2,1) and m is the slope 4, we substitute the values into the equation.
Therefore, the equation of the line tangent to the graph of y = x^2 - 3 at the point P(2,1) is y - 1 = 4(x - 2).
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.
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.
- Find the Derivative of #sec x# using first principle?
- How do you find the equation tangent to #y=x^4-3x^2+2# at Point: (1,0)?
- How do you find the instantaneous rate of change for #f(x)= x^3 +2x^2 + x# for [-1,2]?
- What is the instantaneous velocity of an object moving in accordance to # f(t)= (e^(t-t^2),e^t/t^2) # at # t=2 #?
- What is the equation of the normal line of #f(x)= sinx# at #x = pi/8#?
- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7