3. Students in another class are asked to find the equation of a tangent line of

Question

3. Students in another class are asked to find the equation of a tangent line of a certain function g(r) at the point where x = 1, They give the four answers listed below. All we know about g(x) is that 9) 0 and g'(1) > 0, so we can't find the equation of the tangent line directly. However, it turns out that exactly one of the four answers listed below is correct. Find it by identifying why the other three answers can't be the equation of the tangent line. A. y=(2x + 1)(1-1) + x2 +x-3 B. y=-2(z-1)+1 3(x 1-4 D.

Explanation / Answer

Q3 . A is not a line hence rejected

B has negative slope , rejected

C is not even an equation , rejected

Hence D is the answer

Q2

f(x) = sin(x2+1) / (x2+1)

using d(u/v) = vu' - uv' / v2

df/dx = (x2+1) cos(x2+1) * 2x - sin(x2+1) 2x / (x2+1)2

= 2x ((x2+1) cos(x2+1) - sin(x2+1) ) / (x2+1)2

At x = 0 , Clearly df/dx = 0

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