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Likurg_2 [28]
2 years ago
13

Find the equation of the tangent line. y=(x^2+x-2)^2 at (-1,4)​

Mathematics
1 answer:
Keith_Richards [23]2 years ago
6 0

Compute the derivative of <em>y</em> = (<em>x</em>² + <em>x</em> - 2)² using the chain rule:

d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) d/d<em>x</em> [<em>x</em>² + <em>x</em> - 2]

d<em>y</em>/d<em>x</em> = 2 (<em>x</em>² + <em>x</em> - 2) (2<em>x</em> + 1)

Evaluate the derivative at <em>x</em> = -1 :

d<em>y</em>/d<em>x</em> (-1) = 2 ((-1)² + (-1) - 2) (2 (-1) + 1) = 4

This is the slope of the tangent line to the function at (-1, 4).

Use the point-slope formula to get the equation for the tangent line:

<em>y</em> - 4 = 4 (<em>x</em> - (-1))   →   <em>y</em> = 4<em>x</em> + 8

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What is the answer to Q=1/2p+15, for p​
Mazyrski [523]

Answer: Q=1/2p+15,= p=2q-30= Slope = 1.000/2.000 = 0.500

 p-intercept = -30/1 = -30.00000

 q-intercept = 30/2 = 15

Step-by-step explanation: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    p-(2*q-30)=0  

Solve   p-2q+30  = 0

we have an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  p-2q+30  = 0 and calculate its properties

Notice that when p = 0 the value of q is 15/1 so this line "cuts" the q axis at q=15.00000

 q-intercept = 30/2  =  15

When q = 0 the value of p is -30/1 Our line therefore "cuts" the p axis at p=-30.00000

 p-intercept = -30/1  = -30.00000

Slope is defined as the change in q divided by the change in p. We note that for p=0, the value of q is 15.000 and for p=2.000, the value of q is 16.000. So, for a change of 2.000 in p (The change in p is sometimes referred to as "RUN") we get a change of 16.000 - 15.000 = 1.000 in q. (The change in q is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  1.000/2.000 =  0.500

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Step-by-step explanation:

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