# How do you find the slope and equation of the tangent line to the curve #y=9-2x^2# at the point (2,1)?

Given -

Its first derivative gives the slope of the curve st any given point.

The tangent passes through the point (2, 1)

At x = 2 ; the slope of the given curve is

Slope of the tangent is the same as slope of the curve at point (2,1)

Equation of the line -

Watch the Video

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

To find the slope of the tangent line, we need to find the derivative of the given curve. The derivative of y=9-2x^2 is dy/dx = -4x.

To find the slope at the point (2,1), we substitute x=2 into the derivative: dy/dx = -4(2) = -8.

Therefore, the slope of the tangent line at the point (2,1) is -8.

To find the equation of the tangent line, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

Substituting the values, we have: y - 1 = -8(x - 2).

Simplifying the equation, we get: y - 1 = -8x + 16.

Rearranging the equation, we find the equation of the tangent line to be y = -8x + 17.

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 find average value of function #h(r) = 3 / (1+r)^2# on given interval [1, 6]?
- How do you find the derivative of #f(x)= 9-x^2# using the limit definition at x=2?
- How do you find the equation of the tangent line to the curve #y=(x^2)e^(x+2)# at x=2?
- Using the limit definition, how do you differentiate #f(x)=x^(-1/2)#?
- What is the instantaneous rate of change of #f(x)=1/(x^3-2x+5 )# at #x=0 #?

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