explain If you work alone, you may choose problems of either group. For an extra

Question

explain

If you work alone, you may choose problems of either group. For an extra five appropriate letter for each problem to indicate which problems you are solving one problem from each section. If you wish, you may solve one more max/min different from the first one you solved (i.e. _1 or 2) to reduce the point count from 25 to 20. If you solve two of the same type. I will randomly grade only if the problem statement contains units, your answer must contain units. Tangents and Normals Find an equation for the line tangent to the curve y = 4 - 7.x2 at x = -2 y = 4 - 7(-2)2 = -24 mtan = dy/dx = -14x = -l4(-2)= 28 y = mtan (x -x1) + y1 y = 28 (x - (-2) -24 = 28x + 32 Find the equation of the line normal to the curve y=4 - 7x2 at x = -2 y = 3 - 5 (-1)3 = 8 mtan =dy/dx = - 15x2 = -15 (-1)2 = -15 m = 1/mtan = 1/15 y = m (x - x1) + y1 y = 1/15 (x - (-1)) + 8 = 1/15x+8 1/15

Explanation / Answer

In both problems, As we know equation of y in terms of x and we know point of x through which tangent is passing. So, we need to calculate coordinate of y by plug in value of x in given equation.

Then we are finding slope of tangent through which it is passing. Slope is given by dy/dx. Which is calculated by differentiating equation and plug in value of x in that equation. So, we get m tan in both problems.

then in first problem we are finding equation of tangent passing through(-2,-24) and having slope 28. By using equation

y=m(x-x1)+y1

For problem 2, we have slope of tangent*slope of normal =1

So, we find slope of normal from there. And then find equation similarly like in 1st problem as we know slope and x1,y1.

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