How do you find an equation of the tangent line to the parabola #y=x^2-2x+7# at the point (3,10)?

Answer 1

# y=4x-2#

The gradient of the tangent to a curve at any particular point is give by the derivative of the curve at that point. The normal is perpendicular to the tangent, so the product of their gradients is #-1#

so If #y=x^2-2x+7# then differentiating wrt #x# gives us:

#dy/dx = 2x-2#

When #x=3 => y=9-6+7=10# (so #(3,10)# lies on the curve)
and #dy/dx=6-2=4#

So the tangent we seek passes through #(3,10)# ad has gradient #4# so using #y-y_1=m(x-x_1)# the equation we seek is;

# y-10=4(x-3) #
# :. y-10=4x-12#
# :. y=4x-2#

We can confirm this graphically:

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 parabola y=x^2-2x+7 at the point (3,10), we need to find the slope of the tangent line at that point.

First, we find the derivative of the function y=x^2-2x+7 with respect to x.

The derivative of y=x^2-2x+7 is dy/dx = 2x-2.

Next, we substitute x=3 into the derivative to find the slope at the point (3,10).

dy/dx = 2(3)-2 = 4.

So, the slope of the tangent line at the point (3,10) is 4.

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 into the equation.

y-10=4(x-3).

Simplifying the equation, we get y-10=4x-12.

Finally, rearranging the equation, we find the equation of the tangent line to the parabola y=x^2-2x+7 at the point (3,10) is y=4x-2.

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