What is the equation of the normal line of #f(x)=-2x^3+x^2-2x-1# at #x=-2#?

Answer 1

#y-23=1/30 (x+2)#

First find the slope of the tangent line at the given point. It would be f' (-2).

Thus find #f'(x) =-6x^2 +2x -2 -> f'(-2)= -30# The slope of the normal would be #1/30#

At x=-2, f(x) would be 16+4+4-1 =23. The given point is this (-2, 23)

Equation of the normal line, in point slope form would be

#y-23=1/30 (x+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 2

To find the equation of the normal line at a given point, we need to determine the slope of the tangent line at that point and then find the negative reciprocal of that slope.

To find the slope of the tangent line, we take the derivative of the function f(x).

The derivative of f(x) = -2x^3 + x^2 - 2x - 1 is f'(x) = -6x^2 + 2x - 2.

To find the slope at x = -2, we substitute -2 into f'(x):

f'(-2) = -6(-2)^2 + 2(-2) - 2 = -24 + 4 - 2 = -22.

The slope of the tangent line at x = -2 is -22.

To find the slope of the normal line, we take the negative reciprocal of the slope of the tangent line:

Slope of normal line = -1/(-22) = 1/22.

Now, we have the slope of the normal line and the point of tangency (x = -2, f(-2)).

To find the equation of the normal line, we use the point-slope form:

y - f(-2) = (1/22)(x - (-2)).

Simplifying this equation gives us the equation of the normal line.

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