# How do you find the equation of the tangent line to the curve #y = x^4 + 9x^2 − x#, at (1, 9)?

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

To find the equation of the tangent line to the curve y = x^4 + 9x^2 − x at the point (1, 9), we need to find the slope of the tangent line at that point.

To find the slope, we take the derivative of the function y = x^4 + 9x^2 − x with respect to x.

The derivative of y = x^4 + 9x^2 − x is given by dy/dx = 4x^3 + 18x - 1.

To find the slope at x = 1, we substitute x = 1 into the derivative: dy/dx = 4(1)^3 + 18(1) - 1 = 4 + 18 - 1 = 21.

Therefore, the slope of the tangent line at the point (1, 9) is 21.

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:

y - 9 = 21(x - 1).

Simplifying this equation gives the equation of the tangent line:

y = 21x - 12.

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.

- How do you use the limit definition of the derivative to find the derivative of #f(x)=x+1#?
- What is #lim_(x->oo) x(sqrt(x^2+4)-x)# ?
- How do you find the equation of the line tangent to the graph of #f(x)=xln(2x+3)# at the point (-1,0)?
- What is the equation of the line that is normal to #f(x)=(x+4)^2-e^x# at # x=-3 #?
- What is the instantaneous rate of change of #f(x)=ln(4x^2-6) # at #x=-2 #?

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