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

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

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

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

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.

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.

- What is the equation of the line that is normal to #f(x)= x^3 ln(x^2+1)-x/(x^2+1) #at # x= 1 #?
- What is the slope of #f(x)=-xe^x-x^2# at #x=1#?
- What is the equation of the line tangent to # f(x)=x(x-1)^2-x+3 # at # x=1 #?
- What is the equation of the line tangent to #f(x)=x^2 +6x-9 # at #x=0#?
- How do you find the equation of the tangent line to the curve #f(x) = x^2 + 5x# at x = 4?

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