# How do you find the equation of the line tangent to the graph of #f(x)=x^4# at x=-1?

We also know that at the point on the curve where x =--1, y=1 This point is on the tangent.

1=-4+c gives c=-5 Now sketch the curve and you will see that it makes sense

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 f(x)=x^4 at x=-1, we need to find the slope of the tangent line and the point of tangency.

To find the slope, we take the derivative of f(x) with respect to x. The derivative of f(x)=x^4 is f'(x)=4x^3.

Next, we substitute x=-1 into f'(x) to find the slope at x=-1. f'(-1)=4(-1)^3=-4.

So, the slope of the tangent line at x=-1 is -4.

To find the point of tangency, we substitute x=-1 into f(x). f(-1)=(-1)^4=1.

Therefore, the point of tangency is (-1, 1).

Using the slope-intercept form of a line, y=mx+b, where m is the slope and b is the y-intercept, we can substitute the values we found.

The equation of the line tangent to the graph of f(x)=x^4 at x=-1 is y=-4x-3.

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 tangent line of #f(x) =sqrt(x+15)-x/(x-15)# at #x=5#?
- What is the equation of the tangent line of #f(x)=x^2+5 # at #x=5#?
- What is the average value of the function #f(x) = 1/x^2# on the interval #[1,3]#?
- For #f(x) =(3x-4)/(x-2)^2#, what is the equation of the line tangent to #x =2#?
- What is the equation of the line tangent to # f(x)=-(sin2x)/sin^2 x # at # x=pi/4 #?

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